Methods of operating and implementing wireless communications systems

ABSTRACT

Computerized wireless transmitter/receiver system that automatically uses combinations of various methods, including transmitting data symbols by weighing or modulating a family of time shifted and frequency shifted waveforms bursts, pilot symbol methods, error detection methods, MIMO methods, and other methods, to automatically determine the structure of a data channel, and automatically compensate for signal distortions caused by various structural aspects of the data channel, as well as changes in channel structure. Often the data channel is a two or three dimensional space in which various wireless transmitters, receivers and signal reflectors are moving. The invention&#39;s modulation methods detect locations and speeds of various reflectors and other channel impairments. Error detection schemes, variation of modulation methods, and MIMO techniques further detect and compensate for impairments. The invention can automatically optimize its operational parameters, and produce a deterministic non-fading signal in environments in which other methods would likely degrade.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of application Ser. No. 14/805,400,“METHODS OF OPERATING AND IMPLEMENTING WIRELESS OTFS COMMUNICATIONSSYSTEMS”, filed Jul. 21, 2015, now U.S. Pat. No. 9,634,719, issued Apr.25, 2017; application Ser. No. 14/805,400 claimed the priority benefitof U.S. provisional application 62/027,213 “METHODS OF OPERATING ANDIMPLEMENTING WIRELESS OTFS COMMUNICATIONS SYSTEMS”, filed Jul. 21, 2014;application Ser. No. 14/805,400 was also a continuation in part of U.S.patent application Ser. No. 14/853,911, “OTFS METHODS OF DATA CHANNELCHARACTERIZATION AND USES THEREOF”, filed Dec. 29, 2014, now U.S. Pat.No. 9,444,514 issued Sep. 13, 2016; application Ser. No. 14/805,400 wasalso a continuation in part of U.S. patent application Ser. No.14/751,041 “ORTHONORMAL TIME-FREQUENCY SHIFTING AND SPECTRAL SHAPINGCOMMUNICATIONS METHOD”, filed Jun. 25, 2015; application Ser. No.14/751,041 was a continuation of application Ser. No. 14/341,820,“ORTHONORMAL TIME-FREQUENCY SHIFTING AND SPECTRAL SHAPING COMMUNICATIONSMETHOD”, filed Jul. 27, 2014, now U.S. Pat. No. 9,083,483 issued Jul.14, 2015; application Ser. No. 14/341,820 was a continuation ofapplication Ser. No. 13/117,119 filed May 26, 2011, now U.S. Pat. No.8,879,378 issued Nov. 4, 2014; application Ser. No. 13/117,119 in turnclaimed the priority benefit of U.S. provisional patent application61/359,619, “ORTHONORMAL TIME-FREQUENCY SHIFTING AND SPECTRAL SHAPINGCOMMUNICATIONS METHOD”, filed May 28, 2010; application Ser. No.14/805,400 was also a continuation in part of U.S. patent applicationSer. No. 14/751,049, “SIGNAL MODULATION METHOD RESISTANT TO ECHOREFLECTIONS AND FREQUENCY OFFSETS”, filed Jun. 25, 2015; applicationSer. No. 14/751,049 was a continuation of U.S. patent application Ser.No. 13/430,690, “SIGNAL MODULATION METHOD RESISTANT TO ECHO REFLECTIONSAND FREQUENCY OFFSETS”, filed Mar. 27, 2012, now U.S. Pat. No. 9,083,595issued Jul. 14, 2015; application Ser. No. 13/430,690 in turn claimedthe priority benefit of U.S. provisional patent provisional application61/615,884, “SIGNAL MODULATION METHOD RESISTANT TO ECHO REFLECTIONS ANDFREQUENCY OFFSETS”, filed Mar. 26, 2012; application Ser. No. 13/430,690was also a continuation in part of U.S. patent application Ser. No.13/117,119, “ORTHONORMAL TIME-FREQUENCY SHIFTING AND SPECTRAL SHAPINGCOMMUNICATIONS METHOD”, filed May 26, 2011, now U.S. Pat. No. 8,879,378issued Nov. 4, 2014; application Ser. No. 14/805,400 was also acontinuation in part of U.S. patent application Ser. No. 13/927,091,filed Jun. 25, 2013, “Modulation and equalization in an orthonormaltime-frequency shifting communications system”, now U.S. Pat. No.9,130,638 issued Sep. 8, 2015; which in turn claimed the prioritybenefit of U.S. provisional patent application 61/664,020 filed Jun. 25,2012; the entire contents of all of these applications are incorporatedherein by reference.

BACKGROUND OF THE INVENTION Field of the Invention

This invention is in the field of telecommunications, in particularwireless telecommunications utilizing novel modulation techniques.

Description of the Related Art

Modern electronics communications, such as optical fiber communications,electronic wire or cable based communications, and wirelesscommunications all operate by modulating signals and sending thesesignals over their respective optical fiber, wire/cable, or wirelessmediums or communications channels. In the case of optical fiber andwire/cable, often these data communications channels consist of one (orbetween one and two) dimensions of space and one dimension of time. Inthe case of wireless communications, often these communications channelswill consist of three dimensions of space and one dimension of time.However, for many ground-based wireless applications, often the thirdspatial dimension of height or altitude is less important than the othertwo spatial dimensions.

As they travel through the communications channel, the various signals,which generally travel at or near the speed of light, are generallysubject to various types of degradation or channel impairments. Forexample, echo signals can potentially be generated by optical fiber orwire/cable medium whenever a signal encounters junctions in the opticalfiber or wire/cable. Echo signals can also potentially be generated whenwireless signals bounce off of wireless reflecting surfaces, such as thesides of buildings, and other structures. Similarly frequency shifts canoccur when the optical fiber or wire/cable pass through differentregions of fiber or cable with somewhat different signal propagatingproperties or different ambient temperatures. For wireless signals,signals transmitted to or from a moving reflector, or to or from amoving vehicle are subject to Doppler shifts that also result infrequency shifts. Additionally, the underlying equipment (i.e.transmitters and receivers) themselves do not always operate perfectly,and can produce frequency shifts as well.

These echo effects and frequency shifts are unwanted, and if such shiftsbecome too large, can result in lower rates of signal transmission, aswell as higher error rates. Thus methods to reduce such echo effects andfrequency shifts are of high utility in the communications field.

In previous work, exemplified by applicant's U.S. patent applicationsU.S. 61/349,619, U.S. Ser. No. 13/177,119, U.S. Ser. No. 13/430,690 andas well as U.S. Pat. No. 8,547,988, applicant taught a novel method ofwireless signal modulation that operated by spreading data symbols overa larger range of times, frequencies, and spectral shapes (waveforms)than was previously employed by prior art methods (e.g. greater thansuch methods as Time Division Multiple Access (TDMA), Global System forMobile Communications (GSM), Code Division Multiple Access (CDMA),Frequency Division Multiple Access (FDMA), Orthogonal Frequency-DivisionMultiplexing (OFDM), or other methods).

Applicant's methods, previously termed “Orthonormal Time FrequencyShifting and Spectral Shaping (OTFSSS)” in U.S. Ser. No. 13/117,119 (andsubsequently referred to by the simpler “OTFS” abbreviation in laterpatent applications such as U.S. Ser. No. 13/430,690) operated bysending data in larger “chunks” or frames than previous methods. Thatis, while a prior art CDMA or OFDM method might encode and send units orframes of “N” symbols over a communications link over a set interval oftime, applicant's OTFS methods would typically be based on a minimumunit or frame of N² symbols, or N×M symbols, and often transmit these N²symbols or N×M symbols over longer periods of time. In some embodiments,these data symbols may be complex numbers.

According to this type of scheme, each data symbol from the N² symbol orN×M symbols would typically be distributed, in a lossless and invertible(e.g. reversible) manner, across a plurality of distinguishable (e.g.usually mutually orthogonal) waveforms over a plurality of differenttimes and plurality of different frequencies. These different times andfrequencies were generally chosen according to the time delay andDoppler-shift channel response parameters of the wireless channel. Dueto this lossless spreading, and selection of different times andfrequencies, the information from each data symbol was spread throughoutthe plurality of different times and different frequencies, so that alldata symbols in the frame were equally impacted by the time delay andDoppler frequency shift characteristics of the channel. These methodshelped made the communications channel more “stationary” (e.g.deterministic and non-fading) as a result. That is, within a givenframe, there were no data symbols subject to greater distortion orfading, relative to other data symbols.

In some OTFS modulation embodiments, each data symbol or element that istransmitted was also spread out to a much greater extent in time,frequency, and spectral shape space than was the case for prior artmethods. As a result, at the receiver end, it often took longer to startto resolve the value of any given data symbol because this symbol had tobe gradually built-up or accumulated as the full frame of N² symbols isreceived.

Thus some embodiments of applicant's prior work taught a wirelesscommunication method that used a combination of time, frequency andspectral shaping to transmit data in convolution unit matrices (dataframes) of N·N (N²) (e.g. N×N, N times N) symbols. In some embodiments,either all N² data symbols are received over N spreading time intervals(each composed of N time slices), or none are. In other embodiments thisrequirement was relaxed.

To determine the times, waveforms, and data symbol distribution for thetransmission process, the N² sized data frame matrix could, for example,be multiplied by a first N·N time-frequency shifting matrix, permuted,and then multiplied by a second N·N spectral shaping matrix, therebymixing each data symbol across the entire resulting N·N matrix. Thisresulting data matrix was then selected, modulated, and transmitted, ona one element per time slice basis. At the receiver, the replica matrixwas reconstructed and deconvoluted, revealing a copy of the originallytransmitted data.

For example, in some embodiments taught by U.S. patent application Ser.No. 13/117,119, the OTFS waveforms could be transmitted and received onone frame of data ([D]) at a time basis over a communications link,typically processor and software driven wireless transmitter andreceiver. All of the following steps were usually done automaticallyusing at least one processor.

This first approach used frames of data that would typically comprise amatrix of up to N² data elements, N being greater than 1. This methodwas based on creating an orthonormal matrix set comprising a first N×Nmatrix ([U₁]) and a second N×N matrix ([U₂]). The communications linkand orthonormal matrix set were typically chosen to be capable oftransmitting at least N elements from a matrix product of the first N×Nmatrix ([U₁]), a frame of data ([D]), and the second N×N matrix ([U₂])over one time spreading interval (e.g. one burst). Here each timespreading interval could consist of at least N time slices. The methodtypically operated by forming a first matrix product of the first N×Nmatrix ([U₁]), and the frame of data ([D]), and then permuting the firstmatrix product by an invertible permutation operation P, resulting in apermuted first matrix product P([U₁][D]). The method then formed asecond matrix product of this permuted first matrix product P([U₁][D])and the second N×N_matrix ([U₂]) forming a convoluted data matrix,according to the method, this convoluted data matrix could betransmitted and received over the wireless communications link by:

On the transmitter side, for each single time-spreading interval (e.g.burst time), the method operated by selecting N different elements ofthe convoluted data matrix, and over different said time slices in thistime spreading interval, using a processor to select one element fromthe N different elements of the convoluted data matrix, modulating thiselement, and wirelessly transmitting this element so that each elementoccupies its own time slice.

On the receiver side, the receiver would receive these N differentelements of the convoluted data matrix over different time slices in thevarious time spreading intervals (burst times), and demodulate the Ndifferent elements of this convoluted data matrix. These steps would berepeated up to a total of N times, thereby reassembling a replica of theconvoluted data matrix to the receiver.

The receiver would then use the first N×N matrix ([U₁]) and the secondN×N matrix ([U₂]) to reconstruct the original frame of data ([D]) fromthe convoluted data matrix. In some embodiments of this method, anarbitrary data element of an arbitrary frame of data ([D]) could not beguaranteed to be reconstructed with full accuracy until the convoluteddata matrix had been completely recovered.

U.S. patent application Ser. No. 13/117,119 and its provisionalapplication 61/359,619 also taught an alternative approach oftransmitting and receiving at least one frame of data ([D]) over awireless communications link, where again this frame of data generallycomprised a matrix of up to N² data elements (N being greater than 1).This alternative method worked by convoluting the data elements of theframe of data ([D]) so that the value of each data element, whentransmitted, would be spread over a plurality of wireless waveforms,where each individual waveform in this plurality of wireless waveformswould have a characteristic frequency, and each individual waveform inthis plurality of wireless waveforms would carry the convoluted resultsfrom a plurality of these data elements from the data frame. Accordingto the method, the transmitter automatically transmitted the convolutedresults by shifting the frequency of this plurality of wirelesswaveforms over a plurality of time intervals so that the value of eachdata element would be transmitted as a plurality of frequency shiftedwireless waveforms sent over a plurality of time intervals. At thereceiver side, a receiver would receive and use a processor todeconvolute this plurality of frequency shifted wireless waveforms sentover a plurality of times, and thus reconstruct a replica of at leastone originally transmitted frame of data ([D]). Here again, in someembodiments, the convolution and deconvolution schemes could be selectedso such that an arbitrary data element of an arbitrary frame of data([D]) could not be guaranteed to be reconstructed with full accuracyuntil substantially all of the plurality of frequency shifted wirelesswaveforms had been transmitted and received. Between frames, the samepatterns of time shifts and frequency shifts may repeat, so betweenframes, these time shifts and frequency shifts can be viewed as beingcyclic time sifts and cyclic frequency shifts.

Within a given frame, however, although the time shifts and frequencyshifts may in some embodiments also be cyclic time shifts and cyclicfrequency shifts, this need not always be the case. For example,consider the case where the system is transmitting an M×N frame of datausing M frequencies, over N time periods. Here for each time period, thesystem may simultaneously transmit M OTFS symbols using M mutuallyorthogonal carrier frequencies (e.g. tones, subcarriers, narrow bandsubcarriers, OFDM subcarriers, and the like). The OFTS carrierfrequencies (tones, subcarriers) are all mutually orthogonal, andconsidering the N time periods, are also reused each time period, butneed not be cyclic.

In other embodiments, the methods previously disclosed in U.S. patentapplication Ser. Nos. 13/927,091; 13/927/086; 13/927,095; 13/927,089;13/927,092; 13/927,087; 13/927,088; 13/927,091; and/or provisionalapplication 61/664,020 may be used for some of the OTFS modulationmethods disclosed herein. The entire contents of U.S. patent applicationSer. Nos. 13/927,091; 13/927/086; 13/927,095; 13/927,089; 13/927,092;13/927,087; 13/927,088; 13/927,091; 14/583,911; 62/027,213 and61/664,020 are incorporated herein by reference in their entirety.

BRIEF SUMMARY OF THE INVENTION

In some embodiments, the present disclosure discusses variouscommunication technology products, processes and systems that areparticularly useful for multiuser, point-to-point, point-to-multipoint,meshed, cellular fixed and/or mobile communications. To do this, theinvention often makes use of the simultaneous modulation of discreteinformation symbols across multiple modulation dimensions (e.g. two ormore modulation dimensions such as time-shift dimensions,frequency-shift dimensions, space-shift dimensions,polarization-rotation dimensions, scale dimensions, and the like). Inother embodiments, the invention may make use of novel modulationtechniques derived from representation theory, at times assisted byvarious combinations with MIMO (e.g. multiple-input and multiple outputantennas) or other wireless beam forming technology. Although in thisspecification, wireless media are most frequently used as specificexamples, in alternative embodiments, the concepts discussed herein mayalso be applied to other types of media, including various types ofnon-wireless media.

The invention is based, in part, on the observations and insight thatpresent day communications systems, such as wireless systems, are toooften plagued by apparently unpredictable (e.g. apparentlynon-deterministic) signal fading and interference. Consider wirelesscell phone communications. These operate by transmitting wirelesssignals (e.g. radio signals) through a “communications channel”consisting of three dimensional space and time (here we will at presentneglect the effects of air, clouds, rain, and the like. Also note thatthe height dimension is often minimal relative to the other dimensions,and thus often a two dimensional space and time model of thecommunications channel is adequate). Envision this taking place in anurban environment. As a cell phone changes position, the signals to andfrom the cell phone and a cell phone base station can be subject toapparently unpredictable amounts of distortion and interference as thewireless signals are reflected off of various objects (e.g. buildings,bridges, moving vehicles) and the like. We can view the sum total ofthese various objects as imposing a “structure” on the communicationschannel.

Each reflection produces various time-delayed “echo” wireless signals.Depending on the relative movement of the cell phone, the base station,and various intermediate reflectors (e.g. moving vehicles), thesevarious echo reflections can also be frequency shifted as well (e.g.Doppler shifted). By the time that all these various time-delayed andfrequency shifted signals arrive at a particular receiving antenna (beit a cell phone antenna or base station antenna), the various signalswill be distorted and will often be subject to an apparentlyunpredictable (e.g. apparently non-deterministic) changes in signalintensity, resulting in fading and other communications impairments.

These effects are often called the “channel response” of acommunications channel. Prior art in the field tended to treat thesetypes of signal fading and other distortion as being inherentlynon-deterministic and essentially impossible to solve for. Prior artinstead tended to teach statistical approaches to merely describe thechances of such fading and other problems occurring. Thus prior artmethods tended use statistical parameters (e.g. typical fading durationtimes, typical length of time that a signal would remain coherent,typical frequency bandwidth that a wireless signal would remaincoherent, and the like) to try to cope with these issues.

By contrast, the present invention is based, in part, on the insightthat modern electronics (e.g. processing capability and speed) now makealternative approaches possible. In particular, the invention is basedon the concept of transmitting data, often in the form of short timeduration bursts, that are modulated in a novel manner that is intendedto both expose the underlying structure (e.g. distribution ofreflectors, relative velocity of transmitters, receivers, reflectors,and the like) of the communications channel, as well as to make it morefeasible to (in effect) solve for the distorting effects of theseobjects as wireless signals propagate through the communicationschannel. In essence, this “solving” allows the system to sort out manyof the reflections and other signal shifts, and to intelligently correct(e.g. deconvolute) the various distortions (convolutions) imposed on thesignal by the data channel structure.

According to the invention, wireless signals are often modulatedaccording to a series of short bursts and various time shifts intendedto help expose relative distances at which signal reflectors may bedisposed in the communications channel. At the same time, the inventionwill often also modulate the wireless signals according to a series offrequency shifts intended to also help expose the relative velocities ofthe receiver(s), transmitter(s) and reflectors operating in thecommunications channel. Other types of simultaneous signal modulation,such as according to space (e.g. use of multiple antennas) or othersignal parameters (e.g. polarization) may also be used as well.

The invention is also based, in part, on the insight that the better theunderlying structure of a communications channel can be characterized,the better the overall performance. Thus use of multiple antennas canhelp characterize the underlying structure of a communications channel(e.g. using parallax effects to better locate reflectors), as well asaiding in beam formation to direct wireless energy transmitters orreceivers in more advantageous patterns. Because not all reflectorsreflect radio waves in the same way (some reflectors impart polarizationchanges), use of polarized wireless signals can also help bettercharacterize the underlying structure of a communications channel, aswell as to help select specific wireless signal polarization modes thatmay be more useful given the particular structure of the communicationschannel at hand.

Other methods may also be used to improve the performance of the systemstill further. Some of these other methods can include methods ofsending and receiving data by also packaging data symbols intomatrix-like data frames. These matrix like data frames can often beconfigured with pilot signals to help the system better characterize thestructure of the data channel, as well as often configured with variouserror codes that can help the system detect problems and take correctiveaction. In addition to standard error correcting purposes, such errorcodes can also be helpful in informing the system when its underlyingunderstanding of the structure of the data channel may be sub-optimum,and when further optimization (e.g. sending more pilot symbols,configuring various time-frequency-polarization, multiple antennaconfigurations, and the like) would be useful. Various methods ofinterleaving data frames, adjusting burst type, to optimize other systemcharacteristics such as latency (e.g. time delay needed to transmit agiven set of data) will also be discussed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an abstracted model of at least one wireless transmitter,receiver (each of which may have their own velocities and locations),operating relative to at least one wireless reflector (which may haveits own location, various coefficients of reflection and velocities) ina data channel (here only two dimensions of space are shown, and thetime dimension is shown by the velocity arrow of the reflector).

FIG. 2 shows how OTFS pilot symbol waveform bursts, transmitted at aparticular OTFS time and frequency offset bin, and in some embodimentssurrounded by various “clear” OTFS time and frequency bins, can be usedto help determine channel response parameters.

FIG. 3 shows use of a mixed OTFS data frame with some portions of thedata frame being utilized for OTFS pilot symbol waveform bursts forchannel response parameter purposes, and other portions being utilizedfor the OTFS “data payload”.

FIG. 4 shows an OTFS MIMO embodiment in which a MIMO OTFS transmitterforms a wireless beam of energy directed towards an OTFS receiver ofinterest. FIG. 4 also shows how use of OTFS pilot symbol waveform burstscan help the system determine the channel response parameters of thesystem, and hence help direct the MIMO OTFS transmitter beam towards theOTFS receiver.

FIG. 5 shows an alternative OTFS MIMO situation, where a new reflector(reflector 2) is now preventing wireless signals from traveling directlyfrom the MIMO OTFS transmitter to the OTFS receiver. The OTFS system canautomatically detect the problem (here by using OTFS pilot symbols,possibly assisted by the invention's error detection methods, to detectchanges in the channel response parameters) and then direct thetransmitter's MIMO antennas to form the transmitted beam in thedirection of a useful reflector, thus making contact with the receiverusing indirect reflected signals.

FIG. 6 shows another alternative OTFS MIMO situation, similar to thatshown in FIG. 5 above. Here however, the OTFS receiver is a MIMO OTFSreceiver, and the receiver has used the changes in the channel responseparameters to direct the receiver's MIMO antennas to preferentiallyreceive in the direction of the useful reflector.

FIG. 7 shows how the various embodiments of the invention—OTFStransmitters, OTFS receivers, modifying OTFS time shifts, frequencyshifts, polarization, burst characteristics, use of error codes, pilotsymbols, MIMO antennas, maps of channel response parameters and the likecan all work together, either all combined, or with only someembodiments implemented, to produce a unified OTFS wirelesscommunications system designed to provide robust and fade resistantcommunications even when operating in a difficult and constantlychanging environment.

DETAILED DESCRIPTION OF THE INVENTION

As previously discussed, the invention is based in part on the insightthat in contrast to prior art methods that tended to view variations insignal strength (e.g. occasional signal fading, how long a signalremains coherent, how large a range of signal frequency ranges can beexpected to be coherent) as something that can only be handled bystatistical methods, superior results can be obtained if the underlyingstructure of a communications channel is exposed, and the various causesof signal distortion (e.g. various reflections, frequency shifts, othershifts and the like) are instead sorted out or “solved for”.

Since communication channels are used to transmit data, throughout thisdisclosure, generally communication channels will referred to as “datachannels”. The main focus of this disclosure will be on wireless datachannels that transmit data (often using radio signals of variousfrequencies up into the microwave frequencies and beyond) though threedimensions of space (often on earth, where the “space” may be filledwith air and even other natural airborne objects such as clouds,raindrops, hail and the like) and one dimension of time. However atleast a number of the concepts disclosed herein can also be used forother data channels operating in other media (e.g. water, conductivemetals, transparent solids, and the like). In some embodiments, somespatial dimensions, such as height, may be less important. Thus forgenerality, the invention will often be referred to as operating using amulti-dimensional data channel comprising at least two dimensions ofspace and one dimension of time. It should be understood, however thatalthough often the invention will operate in three dimensions of spaceand one dimension of time; embodiments that only operate in oneeffective dimension of space and one dimension of time are alsocontemplated.

The invention makes use of modern electronic components, such asprocessors (e.g. microprocessors, which can even be commonly usedprocessors such as the popular Intel x86 series of processors), anddigital signal processors; and often will employ modern softwareconfigured wireless transmitters and receivers which can, for example,be implemented by various field programmable gate arrays (FPGA). Herethe methods of Harris, “Digital Receivers and Transmitters UsingPolyphase Filter Banks for Wireless Communications”, IEEE transactionsvolume 51 (4), April 2003, pages 1395-1412. Application specificintegrated circuits (ASICs) and other types of devices and methods mayalso be used.

Although the invention has many embodiments, some of which will bediscussed at length herein, at the core, many of these embodiments canbe considered to be based on an automated method of transmitting(usually wirelessly transmitting) a plurality of symbols (often OTFSsymbols, often carrying data) through a multi-dimensional data channel(often these multiple dimensions will be at least one or two, and oftenthree dimensions of space and one dimension of time) between at leastone wireless transmitter and at least one wireless receiver.

One unique aspect of the invention is that it often wirelessly transmitsdata symbols in the form of orthogonal time shifted and frequencyshifted wireless waveforms, often referred to in this specification asOTFS symbols and OTFS waveforms. OTFS symbols and OTFS waveforms can beimplemented by various methods, some of which were previously disclosedin parent applications U.S. 61/349,619, U.S. Ser. No. 13/177,119, U.S.Ser. No. 13/430,690 and as well as U.S. Pat. No. 8,547,988; all of whichare incorporated herein by reference in their entirety. Please refer tothese earlier disclosures for a more detailed discussion of variousaspects of OTFS waveform technology, as well as a more detaileddiscussion as to various methods to implement OTFS symbols and dataframes.

To briefly summarize some aspects of these earlier disclosures, in someembodiments, data symbols intended for transmission as OTFS symbols may,on the transmitter side, be distributed, usually automatically using atleast one processor and appropriate software, over various symbolmatrices or “data frames”. These may be N·N matrices, or even N·Mmatrices (where M is different from N). These symbol matrices or dataframes are then used as input to control the modulation of the system'swireless transmitter(s). Specifically the data symbols intended fortransmission may be used to weigh or modulate a family of time shiftedand frequency shifted waveforms.

This can be done by, for example, at the transmitter using the datasymbols to control the operation of a bank of wireless signal modulators(e.g. QAM modulators, which may be implemented using the previouslydiscussed methods of Harris or other methods). The resulting output can,for example, result in a plurality of bursts of QAM modulated waveforms,over a plurality of frequencies and time shifts, which can later be usedby the receiver to help identify the structure of the data channel (e.g.positions and velocities of various reflectors).

Although these waveforms may then be distorted during transmission,their basic time and frequency repeating structure can be used by thesystem's receivers, along with appropriate receiver based deconvolutionmethods, to correct for these distortions by utilizing the repeatingpatterns to determine the type of deconvolution needed.

To generalize, in the methods described herein, symbols, which cancomprise any of pilot symbol, null symbols, and usually data symbols arearranged into at least one, and often a plurality of symbol frames,sometimes also called planes. The symbols may be a variety of differenttypes of symbols, but often may be represented as complex numbers, oftencomplex integers (e.g. Gaussian integers) and/or QAM symbols. Thesesymbol frames are thus typically two dimensional arrays such as N×N orN×M frames of these symbols, where both N and M are integers greaterthan 1. The system will typically operate on a per symbol frame basis.

Typically, on a per symbol frame basis, at least one processor (usuallya transmitter processor) will spread the information in at least eachdata symbol (in a given symbol frame) across at least all data symbolsin that symbol's frame using a lossless and invertible transformation.Various specific types of lossless and invertible transformations aredescribed herein, but these specific examples are not intended to belimiting. The net result of this transformation process is that at leastfor each set of data symbols in a given data symbol frame or data symbolportion of a frame, a corresponding two dimensional OTFS frame (dataplane) comprising a plurality of OTFS symbols will be generated.Although often, if a given symbol frame has N×M symbols, a correspondingOTFS frame comprising N times M symbols will be generated, this exampleis also not intended to be limiting. These OTFS symbols will then betransmitted in a manner in which (again on a per OTFS frame basis), eachOTFS symbol derived from data symbols in that OTFS frame will be spreadthroughout a plurality of mutually distinguishable (usually because theyare mutually orthogonal) time shifted and frequency shifted wirelessOTFS waveform bursts. These OTFS waveform bursts then traverse the datachannel as discussed elsewhere in this disclosure.

Again to generalize, the wireless receiver(s) will typically thenreceive the now channel convoluted OTFS waveform bursts on a per OTFSframe basis, and after deconvolution, derive at least an approximationof the originally transmitted OTFS waveform bursts, thereby creating anapproximation or replica of the originally transmitted OTFS frame(replica OTFS frame). The receiver can then use at least one processor(typically a receiver processor) and an inverse of the transformation toextract replica symbols from this approximation of the originallytransmitted OTFS frame (replica OTFS frame).

As a consequence of this method (e.g. due to the lossless and invertiblespreading), or as a further constraint on this method, typically atleast for data symbols, an arbitrary (data) symbol cannot be guaranteedto be extracted (i.e. transmitted and received) with full accuracyunless substantially all of the OTFS symbols from that symbol'sparticular frame of OTFS symbols have been transmitted and received.Here “substantially all” will be somewhat dependent on the specifics ofthe situation (frame size, use of pilot symbols, errordetection/correction symbols, and the like), but often will require that80% or more of at least the data symbol derived OTFS symbols besuccessfully transmitted and received. In some limiting situations,where there is no use of pilot symbols or error detection/correctionsymbols, and no redundancy in the data symbols, all OTFS symbols in agiven OTFS frame will need to be successfully transmitted and received.However such lack of robustness is not desirable, and typically thislater situation will be avoided.

FIG. 1 shows an abstracted model of the structure of the data channel(100), in which at least one wireless transmitter (102), receiver (104)(both the transmitter and the receiver have their own respectivevelocities and locations), operating relative to at least one wirelessreflector (106). Each wireless reflector (106) will typically have itsown location, various coefficients of wireless reflection and velocities(108). These transmitters, receivers, and reflector(s) operate in a datachannel that, in the example of wireless communications, can be two orthree dimensions of space (here we are neglecting atmospheric issues)and a dimension of time. The time dimension is exemplified by thevelocity arrow (108) indicating that in this example the reflector (106)is moving. To keep the diagram simple, the transmitter and the receiverare shown as stationary, although in fact they each may have their ownvelocities as well.

In a more basic aspect of the invention, the invention may thus be amethod of using at least one transmitter (102) and at least onetransmitter based processor to wirelessly transmit a plurality ofsymbols as a plurality of OTFS symbols (110). As previously discussed,each OTFS symbol in these plurality of OTFS symbols are generally spreadthroughout a plurality of mutually orthogonal time convoluted (orshifted) and frequency convoluted (or shifted) wireless OTFS waveformbursts, which here will be designated as “originally transmittedwireless OTFS waveform bursts”. The word “burst” is intended todesignate that the modulated waveforms will have limited time duration,typically a small fraction of a second. These small time duration burstsare can be understood as having a secondary function that is a somewhatlike the small bursts or chirps used in echo location and radar; thebursts help the receiver better distinguish the relative locations ofvarious reflectors, and generally assist in later signal deconvolutionat the receiver end.

As these wireless OTFS waveform bursts travel (propagate) through themulti-dimensional data channel (100) (e.g. space between the transmitter(102) and receiver (104) also including any reflectors (106), theoriginally transmitted wireless OTFS waveform bursts (110) generallytravel over at least one path. This at least one path will generallycomprise either a direct path (112) and/or one or more reflected paths(114 a, 114 b).

Thus direct path (112) will generally be created by originallytransmitted wireless OTFS waveform bursts (110) traveling in a generallystraight line (112) from the at least one wireless transmitter (102) tothe at least one wireless receiver (104). These will be termed “directwireless OTFS waveform bursts”.

Similarly reflected paths (114 a, 114 b) will generally be created whenthe originally transmitted OTFS waveform bursts (114 a) reflect (114 b)off of at least one wireless reflector (106) (which may be moving at agiven velocity (108)) before reaching the wireless receiver(s) (104).These reflected waveforms (114 b) will, in this example be both timedelayed and Doppler frequency shifted relative to the direct wirelessOTFS waveform bursts (112). Thus these time delayed and Dopplerfrequency shifted waveforms will be termed “time delayed and Dopplerfrequency shifted reflected wireless OTFS waveform bursts” (114 b) whenthey are received at the wireless receiver (104). Note also that due tothe relative locations and velocities of the transmitter (102) andreceiver (104), even the direct waveforms (112) may be time delayed andfrequency shifted as well, but for now this effect is ignored in thepresent discussion because what mainly matters is that at the receiver,the direct (112) and indirect (114 b) waveforms meet. Because they havedifferent time delays and frequency shifts, they will then engage inconstructive and destructive interference with each other, and this isthe major problem at hand. Of course more generally, direct path timedelays and frequency shifts must also be taken into account.

Returning to the present example, at the wireless receiver(s) (104), theresulting combination of essentially any direct wireless OTFS waveformbursts (112) and any reflected wireless OTFS waveform bursts (114 b)will produce patterns of constructive and destructive interference(which can result in channel fading, among other problems). Thiscombination will be termed “channel convoluted OTFS waveform bursts”.

Such patterns of constructive and destructive interference can produceproblems and fading regardless of the modulation scheme of the wirelesswaveforms being transmitted. Prior art merely attempted (using variousstatistical methods) to determine the likelihood of such problems tothen configure system settings so that wireless systems could continueto communicate, but at a lesser degree of functionality. By contrast thepresent art teaches an alternative approach.

The prior art, for example, would teach the that since the reflectedenergy from reflected signal (114 b) is often lower than the directsignal (112), then one (suboptimal) solution would be to reduce thesensitivity of the receiver (104) and continue to receive direct signal(112) at a lower level of efficiency.

Alternatively, as is often done for some OFDM systems, echo effects canbe mitigated by splitting the information over a large number ofnarrow-band OFDM subcarriers, each carried by mutually orthogonal tones,but transmitting information on each subcarrier at a relatively slowrate. But this doesn't really “solve the problem”, just mitigates it,because each OFDM subcarrier is still affected by reflected signals, andthus must still operate at a slower than optimum rate. Some OFDM systemsalso try to avoid the echo effect problem by use of cyclic prefix typewaveforms, which slows down the data carrying rate of each OFDMsubcarrier still further.

By contrast, the presently disclosed art teaches something more akin tocontinuing to operate, at an almost normal level of functionality,despite such patterns of constructive and destructive interference. Thisis done by, for example, sending waveforms capable of letting thereceiver (104) analyze the existence and properties of intermediatereflector (106). This in turn lets the receiver adapt its operation toalso make use of wireless energy from reflected signal (114 b). Inessence, the invention's methods can instruct the receiver not todiminish its sensitivity, but rather to expect some reflected signals(114 b) to be similar to the direct signals (112), but offset by acertain time delay and frequency.

Thus rather than diminish the sensitivity of receiver (104), theinvention instead directs the receiver to process the received signal tosupplement the direct signal (112) with appropriately adjusted time andfrequency shifted signal (114 b). This allows the system to operate atnearly full efficiency, and in a deterministic manner that iseffectively non-fading because the signal from the transmitter (102) isalmost never lost, just transformed into a different form (e.g. moreinto waveforms (114 b) depending on the location and velocity of thereflector(s) (106).

Thus according to many embodiments of the methods disclosed herein,receiver(s) (104) will receive these channel convoluted OTFS waveformbursts (e.g. any combination of 112 and 114 b), and will usually useit's at least one receiver based processor to deconvolute these channelconvoluted OTFS waveform bursts. That is, the receiver will correct forthe distortions caused by, for example, the constructive interference ofsignals (112) and (114 b) by analyzing these signals and applying atleast the appropriate time delays and frequency corrections in order toallow signals (112) and (114 b) to be correctly analyzed by receiver.The OTFS receiver (104) understands that (112) and (114 b) are merelydifferent forms of the same signal. The receiver thus properly receivesthese symbols in a deterministic and generally fade resistant mannereven as the position and or velocity of reflectors such as (106) change.

In some embodiments, this deconvolution process can be done by using atleast one processor (often a receiver based processor) to characterizethe structure of the channel (100). Here, for example, this at least oneprocessor can be used to automatically determine channel responseparameters of this multi-dimensional data channel (100) between thewireless transmitter(s) (102) and the wireless receiver(s) (104).

Here of course, as previously described, the “channel responseparameters” of the multi-dimensional data channel (100) are created byat least the relative positions, relative speeds, and properties of thewireless transmitter(s) (102), wireless receivers (104), and the variouswireless reflector(s) (106), or by other non-reflecting signalattenuator objects (not shown). Essentially, the channel responseparameters allow the receiver (104), for example, to understand that x %of the signal received at the receiver (104) is signal (114 b) that hasbeen frequency shifted by factor “y” and time shifted by factor “z” dueto the velocity (108) and location of reflector (106); and to furtherknow (in this example) that the remainder of the signal received byreceiver (104) is direct signal (112) that either is not time shifted orfrequency shifted, or else is at least time shifted and frequencyshifted to a different extent. This allows the receiver to in essencegenerate a deconvolution model to “solve” for what the original signal(110) really was.

Putting this in alternative language, the wireless receiver(s) (104)will determine the channel response parameters (often by methods to bedescribed shortly) and use these channel response parameters (and oftenat least one receiver based processor) to deconvolute the receivedchannel convoluted OTFS waveform bursts (combination of 112 and 114 b),and thereby derive at least an approximation of the originallytransmitted OTFS waveform bursts (110).

Often after this deconvolution process is done, the receiver can alsouse at least one processor to then mathematically extract (e.g. solvefor, determine) the plurality of OTFS symbols from the receiver basedapproximation of the originally transmitted OTFS waveform bursts (110).For these purposes, often the matrix math based methods of applications61/349,619, Ser. Nos. 13/177,119, 13/430,690 and as well as U.S. Pat.No. 8,547,988; all of which are incorporated herein by reference intheir entirety can be used. Other methods, including analog methods,numeric approximation methods, and the like, may be also be used forthese purposes. Once the various OTFS symbols have been determined atthe receiver, by whatever method, the system will have then transmittedat least some of the original OTFS symbols between the wirelesstransmitter(s) (102) to the wireless receiver(s) (104).

In addition to the matrix math methods discussed above, alternativevariations on these methods may also be practiced. In some embodiments,the previously expressed (e.g. applications 61/349,619, Ser. Nos.13/177,119, 13/430,690 and as well as U.S. Pat. No. 8,547,988)preference for transmitting OTFS data symbols in the form of OTFS dataframes or data planes composed of N×N data symbol matrices, andsubsequently at the receiver retrieving the transmitted data symbols byinverting the transmitted N×N matrices, can be relaxed and/orsupplemented by alternative methods.

Alternative OTFS Data Frame Methods

In an alternative process, the methods described above may beimplemented by transmitting a plurality of OTFS symbols by spreadingeach OTFS symbol through a series of N time convoluted (or shifted), andM frequency convoluted (or shifted) mutually orthogonal waveform bursts.In this embodiment, again both N and M will each be integers greaterthan 1, and N does not have to equal M. This alternative method thuspackages the OTFS symbols in the form of one or more (often a pluralityof) OTFS data planes (here planes and frames will often be usedinterchangeably), each comprising an N·M matrix of mutually orthogonaltime convoluted (or shifted) and frequency convoluted (or shifted)waveform bursts. This process is thus capable of transmitting up to n·mdifferent OTFS symbols per OTFS data plane. Here the main constraint isthat at least in the absence of noise or other form of data corruption,each OTFS data plane must in principle be capable of being analyzed(e.g. solved) by at least one processor (usually a receiver processor).The results of this analysis process should be that each OFTS symbol inthe plurality of up to N·M different OTFS symbols in any given OTFS dataplane can be reconstructed (e.g. determined).

This alternative N·M rectangular matrix formulation of OTFS data planesthus differs from the earlier N·N (or N×N) OTFS data planes in that if,for example, M>N, then there will be extra OTFS symbols that maytransmitted using either a greater extent of time shifting or a greaterextent of frequency shifting than would be the case in an N·N datamatrix. These extra OTFS symbols can be used to transmit more usefuldata (e.g. transmit a greater data payload), or alternatively may beused to for other purposes. Some of these other purposes include helpingthe system achieve better time synchronization, better error correction.This approach can also be useful in situations where the problem of timedelays on the channel are greater than the problem of Doppler frequencyshifts, or the problem of Doppler frequency shifts are greater than theproblem of time delays, and more resolution is desired in one dimension(e.g. time delay or frequency shift) than the other dimension (e.g. timedelay or frequency shift). As will be discussed below, in someembodiments, the extra rows or columns or both may also be used totransmit pilot signals to help determine channel responseparameters/deconvolution parameters.

There are otherwise a number of different ways to reconstruct ordetermine each OTFS symbol. As previously discussed, in addition to thematrix math methods previously discussed in applications 61/349,619,Ser. Nos. 13/177,119, 13/430,690 and as well as U.S. Pat. No. 8,547,988,other methods, including numeric approximation methods, and even analogcomputational methods, may be allowed, although generally digitaloperations that can be performed using a processor or digital signalprocessor are preferred.

Acquiring or Initially Characterizing the Data Channel ResponseParameters

As previously discussed, the system operates using OTFS waveforms thatare designed to help elucidate the underlying structure of the datachannel (100), and that are transmitted in short bursts (110). The OTFSreceiver (104) is generally designed to listen to these various shortbursts of OTFS waveforms (110), and in effect make use of the fact thatthere are repeating echo patterns (e.g. echo 114 b) and repeating timedelay patterns (e.g. caused by the difference in signal travel timebetween direct path (112 and indirect path 114 a+114 b) and repeatingfrequency shifts (e.g. caused by reflector velocity 108, as well aspossible differences in velocity between transmitter (102), receiver(104) and reflector (106) in the OTFS waveforms to make inferences aboutthe structure of the data channel.

It is not necessary that the receiver make a full determination aboutall of the positions, speeds, and the coefficients of wirelessreflection of each and every reflector that may exist in the datachannel, and it may not even be necessary to make a full determinationof the exact relative location and speeds of the wireless transmitterand receiver. However to work well, the receiver should at least obtainenough information about at least the major sources of reflection andenough information about the major sources of various time delay andfrequency shifts, in order to determine the channel response parametersof the channel. These channel response parameters can be viewed as anoperator that distorts the original OTFS signal bursts (110) in a mannerthat mimics the actual signal distortion as detected by the receiver. Inessence, the channel response parameters can be viewed as a mathematicalmodel that replicates, hopefully reasonably closely, what the channelstructure did to the original OTFS wireless waveforms as these waveformstraveled along the various channel paths to the receiver.

In the case of FIG. 1, if the receiver and transmitter were bothstationary, then the channel response parameters would simply be that x% of the original OTFS waveforms were both delayed by a time factor of[(distance 114 a+distance 114 b−distance 112)]/c, where c is the speedof light, as well as Doppler frequency shifted according to a factor ofthe reflector velocity 108. Here x % is in part a function of thecoefficient of wireless reflection of reflector 106. Other factors wouldalso include the relative orientation of reflector (106), the distancebetween the reflector 106 and the transmitter 102, as well as therelative distance between the transmitter 102 and the receiver 104according to an inverse square law formula.

Note however that as we dial in additional variables such the relativelocations and velocities of the receiver and transmitter, and as well asother reflectors with their own coefficients of reflection, velocities,and relative locations, the channel response parameters soon become verycomplex. However because the OTFS wireless signals are constructed tohave repeating patterns of time delays and frequency offsets, the uniqueability of the OTFS system is that the OTFS waveforms can be structuredto contain enough information to allow the receiver to get a reasonablygood estimate of the channel response parameters of at least the majorsignal distortion factors in real life situations.

Once the channel response parameters have been obtained, the next step,obtaining deconvolution parameters (previously discussed in parentapplication Ser. No. 13/430,690 and again incorporated herein byreference) can be viewed as essentially determining an inverse operatorthat in effect deconvolutes or equalizes the distorted (e.g. channelresponse parameter convoluted) OTFS signals back into at least anapproximate version of the original OTFS waveforms. In essence, if thechannel response parameters are the evil twin that causes harm to theOTFS waveforms, the deconvolution parameters are the good twin thatundoes the harm. Mathematically, the two are like two sides of the samecoin—one is the inverse of the other, and knowing one also allows you todeduce the other.

In engineering terms, signal deconvolution is often referred to as“equalization”, and the devices (be they hardware or software running onprocessors) that perform this equalization function are often referredto as equalizers.

Although strictly speaking an optional step, in some embodiments, it canbe useful to help determine the channel response parameters of acommunications channel by presenting the channel with a brief andcommonly known (e.g. known to both the transmitter and receiver)calibration input signal such as a sharp pulse (e.g. a Dirac deltafunction like pulse δ) or other defined symbols or set of symbols. Inthis disclosure, such defined calibration symbols and signals will bereferred to as “pilot symbols” and “pilot signals”.

Pilot Signals to Help Determine Channel ResponseParameters/Deconvolution Parameters

In some embodiments, the system will use at least one transmitter(usually using at least one transmitter based processor) to transmit(usually using OTFS waveforms) at least one pilot symbol in the form ofat least one wireless pilot symbol waveform burst at at-least onedefined time and frequency.

Note that according to the invention, there are two general types ofpilot symbols that are possible. In one form or embodiment of theinvention, the pilot symbols, although transmitted according to the sametiming, frequency ranges, and general spectral timing as the OTFS datasymbols, will nonetheless not be subject to the general OTFS data symbolrequirements that the pilot symbols be smeared or distributed over alltransmitted symbols, and over a plurality of time and frequencycombinations, at the transmitter. This is the embodiment generallydiscussed here. These OTFS pilot symbols (or waveforms whentransmitted), might, in an alternative nomenclature could be called“OTFS associated pilot symbols”.

A second form or embodiment of the invention is also possible, however,in which at least some of the pilot symbols are handled by the system inthe same way that the system handles data symbol—where at least somepilot symbols are smeared or distributed, by the transmitter, over aplurality of times and frequencies in the same manner as the OTFS datasymbols. Indeed these OTFS pilot symbol might even be smeared ordistributed in with the OTFS data symbols. Although this later method isless commonly discussed in this disclosure, this alternative approachhas certain utility, and thus also may be used in some embodiments ofthe invention. In this second embodiment, in alternative nomenclature,the pilot symbols could be called “OTFS encoded pilot symbols”, or “OTFSmodulated pilot symbols”.

Generally, however, most of the discussion herein will focus on “OTFSassociated pilot symbols”, and unless otherwise specified, the pilotsymbols and waveforms discussed herein will generally be OTFS associatedpilot symbols.

In this scheme, the direct (e.g. 112) and reflected versions (e.g. 114b) of the at least one wireless pilot symbol waveform burst (e.g. 110)reach the at least one wireless receiver (104) as at least one channelconvoluted pilot symbol waveform burst (e.g. mixture of 110 and 114 b).

An example of one embodiment of these pilot symbol waveform bursts, herewithin an N·M OTFS data frame (here 6×10 is drawn) is shown in FIGS. 2and 3. Here the white circles can represent OTFS time and frequency binswith zero energy, while darker circles can represent OTFS time andfrequency bins with pilot symbols or other OTFS energy and data beingtransmitted in these OTFS time and frequency bins.

In FIG. 2 (200), one original pilot symbol burst (202) is transmitted bytransmitter (102) at time zero and with zero OTFS frequency shift andzero Doppler shift (relative to some standardized base frequency). Aspreviously discussed, some of the energy from this original pilot symbolburst (110, 202) may travel directly to receiver (104) via path (112) ata later time “t” dependent on the distance between transmitter (102) andreceiver (104). However some of the energy from the original pilotsymbol burst (110, 202) may also reflect off of moving reflector (106).Because these waveforms travel a longer distance to reach the receiver(114 a+114 b), the reflected waveforms arrive at a later time. Becausein this example, the reflector (106) is also moving with velocity (108),the reflected waveforms are also frequency shifted by the time that they(208) arrive at the receiver (104). The resulting channel convolutedpilot symbol waveforms as detected by receiver (104) are thusrepresented as the combination of the direct waveforms (112, 206) andfurther time delayed and frequency shifted reflected waveforms (114 b,208).

If, however, nearby OTFS time and frequency bins are kept clear (i.e.zero signals or known reference signals are transmitted), then thecomputational burden on the receiver to determine the channel responseparameters and the corresponding deconvolution parameters is greatlyreduced (simplified). This is because each OTFS time-frequency bin thathas unexpected signal energy can be assumed by the receiver to be resultof some aspect of the channel's structure, and the receiver can alsoassume that for at least a short period of time (possibly only afraction of a second if reflector 106 is moving), all signals in allOTFS time frequency bins will be distorted to the same amount.

By contrast, consider the burden on the receiver (e.g. the receiverprocessor) if the transmitter is transmitting nothing but unknown (tothe receiver) OTFS symbols on all OTFS time and frequency bins as is thecase in FIG. 2 (210). As a result, the receiver (104) will also receivenothing but further unknown (until deconvoluted and solved for) channelconvoluted OTFS symbols on all OTFS time and frequency bins as well(212). This greatly reduces the number of simplifying assumptions thatthe receiver processor can make, and the computational burden is thuscorrespondingly greater. It still may be doable (indeed the earlierpatent applications such as Ser. No. 13/430,690 previously discussedways to do this), but the problem is more complex and the possibility oferror is correspondingly greater.

Thus according to at least some embodiments of the invention, thetransmitter can transmit known pilot symbols (often accompanied atnearby or contiguous OTFS time-frequency bins with known or zero energyOTFS waveform signals). In this situation, then the at least onewireless receiver (104), can receive this at least one channelconvoluted pilot symbol waveform burst (e.g. 206 and 208, again formedfrom the combination of direct signals 112 and reflected signals 114 b),and use at least one processor (nominally a receiver based processor) todeconvolute this at least one channel convoluted pilot symbol waveformburst.

The (usually receiver) based processor can then automatically determinethe channel response parameters of the multi-dimensional data channel(100) between and surrounding (e.g. connecting) the at least onewireless transmitter (102) and at least one wireless receiver (104).

The receiver can then assume that these channel response parameters willbe stable for at least some period of time (at least a fraction of asecond), use these channel response parameters to compute thecorresponding deconvolution parameters, and thus in effect use thesechannel response parameters (or corresponding deconvolution parameters)to further deconvolute these and other received channel convoluted OTFSwaveform bursts.

Thus consider FIG. 3. In this figure, part (302) of the N·M matrix (300)has been reserved by the transmitter and receiver for pilot symbols andsome surrounding clear OTFS time and frequency bins, and part (304)(here a square 6×6 matrix) has been reserved for transmitting standardOTFS data symbols. So transmitter (102) transmits both a pilot signal(306) at a defined OTFS time and frequency bin, as well as a 6×6 matrixof normal OTFS data symbols at a plurality of different time andfrequency bins (304). The OTFS signals (110) then transit though thedata channel (100) according to paths 112 and 114 a and 114 b as before,and a convoluted form of these signals (310) are thus received byreceiver (104).

Here, however, receiver (104) can first solve for the pilot symbolchannel convolution parameters by analyzing the channel convoluted pilotsymbol waveform burst (e.g. 316 and 318, again formed from thecombination of direct signals 112 and reflected signals 114 b). Theprocessor can determine the appropriate deconvolution parameters, andthen apply them to the rest of the received OTFS signals (314).

Error Detection Methods

In some embodiments, it may also be desirable to implement one or moredifferent error correction methods. Here, for example, at least some ofthe transmitted OTFS symbols can be error detection or error correctionand correction OTFS symbols. Here various error detection schemes can beused, which can be very simple parity bits, but often will be morecomplex error detection codes capable of at least some degree ofredundancy and error correction as well. These schemes can includeforward error correction (FEC) codes with error-correcting code (ECC),backward error detection schemes with automatic repeat request (ARQ),and the like. Various schemes such as checksums, hash functions, cyclicredundancy checks, as well as hybrid error schemes such as hybrid ARQ(e.g. combinations of various ARQ and FEC codes can also be used.Methods such as Reed-Solomon codes, Turbo codes, low-density paritycheck codes (LDPC) and other schemes may also be used.

Typically the transmitter (102) will use its transmitter processor toanalyze the data about to be transmitted, and transmit the data as OTFSsymbols with various error correction OTFS symbols included as well. Thereceiver will often use at least one receiver processor to, after atleast some of the various transmitted OTFS symbols have been received,use the error detection or error correction OTFS symbols to, forexample, detect when OTFS symbol transmission errors are exceeding apredetermined maximum acceptable error level. Usually, such a high levelof errors (e.g. exceeding the predetermined maximum acceptable errorlevel) can be taken as an indicator that the channel response parameters(and corresponding deconvolution parameters) have become suboptimum.

Consider for example, FIG. 1 where moving reflector (106) may havechanged position over time due to its velocity (108). The system mayhave originally (possibly only a few seconds or a fraction of a secondearlier) transmitted one or more pilot symbols (202, 306), according tothe schemes illustrated in FIGS. 2 and 3, to that may have adequatelycharacterized the channel response parameters (e.g. determined by 206,208 or 316, 318) of the multidimensional data channel (100) at anearlier time point. However now, possibly only a few seconds orfractions of a second later, reflector (106) may have changed positionor velocity enough so that the earlier channel response parameters (e.g.as determined by 206, 208 or 316, 318) are no longer accurate. One ofthe first ways that this will show up is when the system's errordetection/error correction scheme reports that errors in the errordetection or error correction OTFS codes are now reporting errors thatare starting to exceed a preset limit.

The receiver can use this information to then determine that the channelresponse parameters are now suboptimum. Various types of correctiveaction are possible. The receiver (104) itself, without furthercommunication with the transmitter (102), can attempt on its own torecalculate the channel response parameters and look for an alternateset of parameters with a reduced amount of errors. Alternatively oradditionally, the receiver (104) can also transmit a request to thetransmitter (102) to transmit one or more new pilot symbols (e.g.refresh the process previously shown in FIGS. 2-3), which will allow thereceiver to again calculate a new set of channel response parameters(and corresponding deconvolution parameters) more appropriate to thepresent location and velocity of reflector (106). As yet another scheme,the receiver (104) can also transmit its present set of channel responseparameters, either with or without the receiver's error code results, totransmitter (102). The transmitter in turn could then make use ofknowledge of what the receiver is detecting (e.g. the receiver channelresponse parameters and associated errors) to also change thetransmitters OTFS modulation scheme or other variables (e.g. MIMOantenna configuration, burst characteristics, error codes, polarization,and other schemes as will be discussed).

In this later case, suppose that due to a particular location orvelocity of reflector (106), certain OTFS time delays or frequencyshifts, or combinations of time delays or frequency shifts, were foundto be either unusually good or unusually bad. The transmitter can makeuse of the receiver transmitted channel response parameters andcorresponding error codes to select various combinations of OTFS timeshifts and frequency shifts to either avoid problematic combinations ofvarious time shifts and frequency shifts, or alternatively to favorunusually good (e.g. reduced interference) combinations of various timeshifts and frequency shifts.

In either event, in at least some of these embodiments, the error codescan be used to automatically inform either the receiver or thetransmitter, or both the transmitter and receiver that the channelresponse parameters are suboptimum, and to initiate various types ofcorrective action such as the actions discussed above.

Alternatively and or additionally, the error detection or errorcorrection codes can also be used by the receiver (usually using atleast one receiver processor) to use the error detection or errorcorrection OTFS symbols to automatically correct errors in other OTFSsymbols.

Interleaving of Different OTFS Burst Types and Data Frame Types

The OTFS system operates, in part, by a modified form of echo locationthat uses bursts of OTFS waveforms to better characterize the structureof the data channel, and better estimate channel response parameters andcorresponding deconvolution parameters. Here some of the aspects of thetime length of the various OTFS wireless waveform bursts, as well asvarious ways in which OTFS symbols can be packaged into various dataframes for subsequent transmission, will be discussed in more detail.

As a general rule, often the plurality of mutually orthogonal timeshifted and frequency shifted wireless OTFS waveform bursts can bevaried and selected by the system (often automatically by thetransmitter's processor, sometimes using information obtained from thereceiver). Some of the ways that the OTFS waveform bursts can beselected can include the desired time latency of the system (e.g. howfast can the system transmit useful data between the transmitter and thereceiver), the bandwidth allocated to the OTFS waveforms (here,regulatory considerations, such as bandwidth allowed by governmentalagencies such as the Federal Communications Commission (FCC) may behighly relevant). As previously discussed, the OTFS waveforms may alsobe varied according to the observed or anticipated channel responseparameters.

There is not necessarily a “one size fits all” criteria here, and evenwithin a communications session between the same transmitter (102) andthe same receiver (104), some OTFS symbols may be transmitted accordingto a first set of selection criteria, while other OTFS symbols may betransmitted according to a different set of selection criteria.

For example, in some embodiments, the plurality of mutually orthogonaltime shifted and frequency shifted wireless OTFS waveform bursts may becharacterized by burst time durations βt that can vary according tovarious factors such as the desired transmission latency time and/or thespatial distribution of reflectors in said communications channel. Forexample, if latency is not a problem, and there are relatively fewreflectors (106) in the communications channel, it may be desirable tochoose longer burst time durations because the in-between each burstwith time length βt will normally be some quiet time δt where little orno data is being transmitted. Thus choosing longer bursts can helpminimize quiet time δt. Alternatively if there are a lot of reflectors(106) in the data channel, or if lower latency is preferred it may bemore important to use short burst times βt to help the system bettercharacterize the channel response parameters, even though the overalldata transmission rate in bits per second may be lower.

Similarly the frequency bandwidth of the bursts (e.g. burst frequencybandwidth) 6 f can also be varied. In addition to changing thisaccording to government regulations and commercial considerations, theburst frequency bandwidth may also be varied by the system (oftenautomatically) according to factors such as the anticipated or observeddistribution of speeds and locations of various receivers, transmitters,and reflectors in the communications channel.

Keep in mind that each OTFS burst will be composed of a plurality oftime shifted and frequency shifted OTFS waveforms. Increasing the rangeof frequency shifted waveforms in the OTFS signal burst (and hence thefrequency bandwidth δf) will improve the ability of the system to detectand respond to a greater range of velocities of transmitters, receivers,and reflectors. A very restricted OTFS system optimized for ground useonly, for example, might only use a range of frequency shifts designedto accommodate Doppler shifts caused by velocities on the order of 0 to+/−100 miles per hour. It might be deliberately designed to disregardDoppler shifts caused by fast flying airplanes (acting either astransmitters, receivers, or reflectors) traveling at +/−600+ per hourspeeds.

Similarly an OTFS system optimized for rural use might be designed toaccommodate much longer distances and (corresponding range of speed oflight imposed time delays) between transmitters, receivers andreflectors (e.g. 10 miles, 20 miles, 30 miles or more). Here, thedensity of reflectors is low, and the time shifts (due to the speed oflight) involved will be higher. One way to optimize for this situationmay be to use a smaller number of frequency shifts spread out over alonger range of times (needed because of the long distances involved inthis data channel structure), or to employ longer time intervals betweenbursts so that delayed signals and echoes from distant receivers,transmitters, and reflectors can be properly detected and analyzed.

By contrast, an OTFS system optimized for urban use may be designed toaccommodate a high density of reflectors (e.g. many buildings per cityblock) and lower signal path lengths between transmitters and receivers(e.g. 1, 2, 3 miles) and reflectors. Here the bursts might use a largernumber of shorter time shifts (this can give the system a greaterability to discriminate between closely spaced reflectors), but theseparation time between bursts can be shorter because the need for longdistance operation is less.

Additionally, the number of OTFS data symbols transmitted per burst canalso be varied by the system. The number of transmitted OTFS symbols,for example, may vary according to either (It and/or δf. Here again, the(It and/or δf burst characteristics can be selected by the system (againoften automatically, using at least one processor and suitable software)according to various considerations including channel responseparameters, desired transmission latency time, and desired number ofOTFS data symbols to be transmitted per burst.

Multiple-Input and Multiple-Output (MIMO) Antenna Schemes

MIMO (e.g. various Multiple-input and Multiple-output (MIMO) antennaschemes) have been used for wireless communications methods, often forvarious beam forming purposes for a number of years. The basic conceptis to use arrays of either spatially separated transmitting antennas,receiving antennas, or both to direct wireless signals in preferreddirections (e.g. concentrate more wireless energy in the direction ofthe receiver or transmitter).

Some prior art methods also rely on some sort of knowledge of thechannel state information between and surrounding (e.g. connecting) thereceiver and transmitter. Here for example, if a receiver is known (byany method) to be located in a certain direction, then the transmittercan be precoded to form its beam in the direction of the receiver.

The previously discussed OTFS concepts are generally both highlycompatible with various MIMO antenna configurations and schemes, andindeed when combined with MIMO can be used to achieve higher levels ofperformance than was previously possible using prior art wirelesscommunication modulation schemes and MIMO schemes alone.

Because, as previously discussed, OTFS methods allow the underlyingstructure of the data channel, and its corresponding impact on thechannel response parameters, to be very precisely determined, often as afunction of time; this channel response parameter data can be combinedwith MIMO methods to greatly enhance the capabilities of the system.

Using MIMO to Shape the Spatial Distribution of OTFS Wireless Waveforms

FIG. 4 shows a more complex version of the abstract multidimensionaldata channel model (400) previously shown in FIG. 1 (100). Heretransmitter (102 m) is now a MIMO transmitter with four spatiallyseparated antennas, transmitting a plurality of OTFS symbols as aplurality of OTFS waveforms, where one set of waveforms (110 a, 110 b,110 c, 110 d) is from each antenna (110 a, 110 b, 110 c, 110 d). Herethe OTFS MIMO transmitter has been configured to transit the four setsof waveforms in a phased arrangement as to form a beam (402 a) thatdirects the wireless OTFS waveforms preferentially in the direction ofreceiver (104). The wireless reflector (106) moving at velocity (108)remains as per FIG. 1, as do direct paths (112 a) and one or morereflected paths (114 a, 114 b).

Unlike FIG. 1, however, assume that either a second reflector (reflector2) (406 a) is moving in a direction (408) that will eventually (but notyet) block the direct path (112 a) between the MIMO transmitter andreceiver (104); or alternatively assume that either the MIMO transmitter(102 m) or the receiver (104) are moving in the direction of reflector 2(406 a) so as again to eventually have reflector 2 block direct path 112a (but not yet).

In FIG. 4, if the OTFS system was using pilot signals according to themethods previously discussed in FIGS. 2 and 3, then assuming thatreflector 2 is still too far away to make any substantial impact on thesystem, then the resulting channel convoluted pilot symbol waveforms asdetected by receiver (104) can, as per FIGS. 2 and 3, still can berepresented as the combination of the direct waveforms (112 a, 416) andthe time delayed and frequency shifted reflected waveforms (114 b, 418).Here, perhaps due to MIMO beam forming, the intensity of (418) may be abit lower than in FIGS. 1 and 3, but otherwise the situation is much aspreviously shown in FIG. 1 and FIGS. 2 and 3.

In this configuration then, at least one wireless transmitter (here 102m) and/or wireless receiver (either 104 or FIG. 6 104 m) have multipleantennas positioned at different locations generally on or near thelocation of the wireless transmitter or wireless receiver. Here assumethat these multiple antennas share the same velocity as of theirrespective wireless transmitter or wireless receiver(s).

In addition to standard MIMO functionality, the system can performenhanced OTFS MIMO functionality by, for example, using these multipleantennas to do novel MIMO functions. For example, the system can use thepreviously described methods (e.g. pilot symbol bursts and the like) todetermine the channel response parameters of multidimensional datachannel (400). For example, the receiver (104) could transmit itsobserved channel response parameters (e.g. obtained from 416, 418) backto transmitter (102 m) and transmitter (102 m) can use these to furtherdirect its MIMO antennas (110 a-110 d) to send more wireless energyalong direct path (112 a) according to MIMO shaped beam 402 a.Alternatively if receiver (104) is a MIMO receiver then receiver couldalso use its multiple antennas to have higher sensitivity along thedirection of direct path (112 a).

In either case, the OTFS MIMO system can use the channel responseparameters to shape at least the spatial distribution of the transmittedor received wireless waveform bursts.

To really see how OTFS techniques can be used to enhance MIMO (andsynergize well with MIMO) consider now how the OTFS MIMO system canoperate in a different situation shown in FIG. 5.

In FIG. 5, now either the second reflector (now called 406 b) has movedto block the direct path (112 a) between MIMO transmitter (102 m) andreceiver (104), or alternatively the MIMO transmitter (102 m) orreceiver (104) has moved so that reflector (406 b) is now blocking thedirect path (112 a) between the transmitter (102 m) and receiver (104).The only path, or at least main path that remains open is the path (114a, 114 b) where the signals from MIMO transmitter (104 m) now arereflected off of reflector 1 (106), and are both time delayed andDoppler frequency shifted due to the velocity (108) of reflector 1.

Note that as previously discussed for FIGS. 2 and 3, these changes inthe structure of multidimensional data channel (400) can be veryintelligently analyzed using OTFS methods. For example, OTFS pilotsymbol burst techniques would show that there is now almost no energybeing received at the OTFS time shift and frequency shift bin (316) thatearlier corresponded to direct path (112, 112 a); however there arestill relatively strong OTFS signals being received according to thetime delayed and frequency shifted reflected waveforms (114 b, 318). Thesensitivity of such methods can be further improved by using variouserror codes and error detecting thresholds to detect problems far inadvance of full loss of signal on a particular pathway.

Here the OTFS system can use the information from these channelconvoluted pilot symbol waveforms in various ways. In one embodiment,the receiver (104) may again transmit its observed channel responseparameters (e.g. as determined by 316, 318) to MIMO transmitter (104 m)and MIMO transmitter (104 m) (often after suitable analysis of thechannel response parameters using a transmitter processor) can thendirect the MIMO antennas (110 a, 110 b, 110 c, 110 d) and OTFS waveformsto shift the direction of the beam (402 b) to now favor reflection offof reflector (106) and use of indirect path (114 a, 114 b).

Alternatively, as is shown in FIG. 6, if the receiver (104 m) is a MIMOreceiver with its own set of multiple antennas, then receiver (104 m)(usually controlled by at least one receiver processor) can itselfdirectly analyze the channel response parameters, and configure its ownreceiver MIMO antennas (600) to have preferential sensitivity (602) in adirection towards reflector 1 (106) and indirect path (114 b). Of courseeven better results may be obtained if both the receiver and thetransmitter both have MIMO antennas, and both use MIMO methods to formoptimal beams of wireless transmission and optimal directions ofwireless reception.

Once, as detected by various combinations of error detecting techniques,channel response parameter techniques, pilot signals, and the like,interfering reflector 2 (406 b) moves out of position (and this may onlybe a few seconds later, or even quicker), the system can thendynamically reconfigure itself back to the earlier configuration shownin FIG. 4, or other configuration as most appropriate. Indeed, bycontinually reconfiguring itself, often multiple times per second inresponse to changes in the channel response parameters, the OTFS systemcan take active steps to prevent signal fading, and to try to ensurehigh quality signal acquisition over a broad range of adverse andconstantly changing channel structures. At the same, time, because thesystem has continuous high quality knowledge about the channel responseparameters and the structure of the multidimensional data challenge, theneed to use the less satisfactory prior art statistical methods can bereduced or eliminated.

Different Streams from Different MIMO Antennas

In some embodiments, either additionally or alternatively to using MIMOfor beam shaping applications, at least some of the OTFS system'sdifferent MIMO antennas may be used for transmitting and/or receiving,often on a simultaneous basis, different OTFS waveform bursts. Thesemethods can be used to send the capabilities of the OTFS system in orderto send more data over a given period of time.

One natural application of this approach can be, for example, an OTFScellular phone tower (e.g. cell site, cell tower, base transceiverstation, base station, base station site, and the like) communicatingwith multiple OTFS equipped cellular phones. In this specific example,the cellular phone tower may have multiple antennas, however at leastsome of the OTFS equipped cell phones (for example handheld cell phones)may have only one antenna, while other OTFS equipped cell phones (forexample cell phones mounted in a vehicle) may also be MIMO devices withmultiple antennas of their own.

In this embodiment, generally either the wireless transmitter and/or thewireless receiver will have multiple antennas (hence the MIMOdesignation). At least some of these various multiple MIMO antennas willbe positioned at different locations on or near the wireless transmitterand/or receiver. These multiple MIMO antennas will have the samevelocity of their respective associated wireless transmitter or wirelessreceiver.

These multiple antennas (at either the transmitter or receiver) can befurther divided into at least a first subset of antennas and a secondsubset of antennas. Here the system is configured so that the firstsubset of multiple antennas transmits or receives a first set ofwireless OTFS waveform bursts, and the second subset of antennas can(often simultaneously) transmit or receive a second set of OTFS waveformbursts. The first set of wireless OTFS waveform bursts will typicallydiffer from the second set of wireless OTFS waveform bursts.

Note that this later approach can be still be compatible with the MIMObeam shaping approaches discussed previously. For example, consider anOTFS cellular phone tower with eight antennas communicating with twodifferent remote OTFS cellular phones. The OTFS cellular phone towercould, for example, at one time partition four of its antennas tocommunicate, using MIMO beam shaping techniques, with a first OTFScellular phone using a first set of wireless OTFS waveform bursts whilesimultaneously partitioning a different set of four antennas tosimultaneously communicate, using MIMO beam shaping techniques, with asecond OTFS cellular phone using a second set of wireless OTFS waveformbursts. The same cellular phone tower could, perhaps a few secondslater, dynamically reconfigure its MIMO antennas to then simultaneouslytalk to eight different OTFS cellular phones by allocating one MIMOantenna to each different OTFS cellular phone, and so on.

In this application as well, the various OTFS concepts of determiningchannel response parameters, error detection and correction, and thelike can further be used by the MIMO OTFS transmitters and/or MIMO OTFSreceivers to intelligently optimize the allocation of MIMO antennas,OTFS time shifts, OTFS frequency shifts, OTFS burst length, OTFS burstbandwidth, and the like to come up with optimal combinations to handlethe particular situation at hand.

MIMO Full Duplex Operation

The OTFS concepts disclosed herein can be used for both unidirectionalcommunications (only one way), half-duplex communications (e.g.communications in both directions, but only one direction at a time),and full-duplex communications (e.g. communications in both directionsat the same time). Here we will discuss some full-duplex embodiments infurther detail.

In one full-duplex operation embodiment, at least one set of wirelesstransmitters and wireless receivers are configured in a first fullduplex device, and at least one set of wireless transmitters andwireless receivers are configured in a second full duplex device.

Here at least the first duplex device (e.g. a cellular phone tower) is aMIMO device with multiple antennas positioned at different locations onor near the first full duplex device (e.g. the cellular phone tower mayhave multiple antennas). These multiple MIMO antennas will often sharethe same velocity of this first full duplex device (e.g. if the cellularphone tower is stationary, typically the MIMO antennas are stationary).

Note however that in alternative embodiments, other MIMO antennaconfigurations where the MIMO antennas may have their own movement, suchas rotating antennas and the like, are also contemplated. In the presentdiscussion, however we will focus on “stationary” embodiments (e.g. MIMOantennas that share the same velocity as their associatedtransmitter/receiver).

Here, the first duplex device's wireless transmitter(s) and wirelessreceiver(s) are each coupled to at least some of the first duplexdevices MIMO antennas (multiple antennas). The first full duplex devicewill further be configured (usually under processor control withsuitable software) to automatically control the coupling between itsmultiple (MIMO) antennas and its wireless transmitter(s) and wirelessreceiver(s) so as to mitigate interference between the device's ownwireless transmitter(s) and wireless receiver(s).

This is important because often the first device's transmitter(s) andreceiver(s) will be transmitting and receiving to and from the secondfull duplex device at the same time. It is thus undesirable for thefirst device's transmitter(s) to interfere (e.g. have cross-talk) withthe first device's receiver(s). However although this “cross talk” isundesirable, simple methods to mitigate the cross talk by, for example,turning down the sensitivity of the first full duplex device receiver(s)to minimize “cross talk” will also have the undesirable effect of alsoturning down the sensitivity of the first full duplex device receiver(s)to pick up signals from outside transmitters, such as the second fullduplex device transmitter(s).

So the problem is one of minimizing cross-talk, while simultaneouslyalso optimizing the sensitivity of the first device's receiver(s) whilereceiving transmissions from the second full duplex device'stransmitter(s). According to the invention, these problems can beaddressed by various methods, including:

Controlling the coupling between the transmitting and receiving antennasby arranging the distribution of the locations of the first full duplexdevice's multiple (MIMO) antennas. For example, this can be done bypositioning the receiving antennas further away from the transmittingantennas, interspersing the transmitting antennas with other MIMOantennas or other structures in between and surrounding (connecting) thetransmitting antennas and the receiving antennas.

Alternatively or additionally, controlling the coupling between thetransmitting and receiving antennas by controlling (either bydynamically reconfiguring, or else continually operating electricalcomponents) the radio frequency (RF) or electrical coupling between thefirst full duplex device's multiple (MIMO) antennas and at least one ofthe first full duplex devices wireless transmitter(s) or receiver (s).

Or as a third alternative, alternatively or additionally amplifying anddigitizing the RF signals to and from the first full duplex device'smultiple (MIMO) antennas, and using at least one processor (e.g. adigital signal processor) to digitally mitigate theinterference/cross-talk between the transmitting and receiving antennas.

Here, for example, when a transmitter transmits in a full duplex device,not only is there a potential direct path between the transmitter andthe receiver, but there are also various indirect paths, such as echoreflections off of nearby structures, that can also contribute tointerference/cross-talk. Here the invention's OTFS methods can also beused to monitor the status of these various echo reflections. Thusaccording to some full duplex embodiments of the invention, the OTFSmethod derived channel response parameters and equalization methods canbe used to digitally mitigate the interference/cross-talk between thetransmitting and receiving antennas. In some embodiments, this digitalmitigation may be done by using the OTFS method derived channel responseparameters to configure an equalizer configured to correct the receivedsignal for distortions caused by interference/cross-talk from thetransmitter.

Alternatively or additionally, the channel response parameterinformation obtained by OTFS methods may be used by the OTFS transmitterto help mitigate at least some of the more troublesome echo reflectionsthat are causing cross talk. Here the digital mitigation of theinterference/cross-talk between the transmitting and receiving antennascan be done by using the OTFS derived channel response parameters to“precode” the OTFS transmitter transmissions in a manner that mitigatesat least some of the more troublesome, interference/cross-talk causing,echo reflections.

Thus, in this later embodiment, at least one of the of the wirelesstransmitters and wireless receivers will be configured as a first fullduplex device, and at least one of the wireless transmitters andwireless receivers will be configured as a second full duplex device.For at least one of these devices, such as at least the first fullduplex device, this device (in addition to the other techniquesdiscussed above), can also use OTFS methods to help further control thecoupling (cross-talk) and mitigate interference between its own wirelesstransmitter(s) and wireless receiver(s). At the same time, this firstdevice can still while transmit to the second full duplex device, andmaintain the first device's receiver sensitivity for signals from thesecond device's transmitter. Here, as before, the idea is to controlthis coupling (cross-talk) by, either in addition to, or instead ofobtaining the channel response parameters between the first device andthe second device, also using OTFS methods to obtain the “self-channelresponse parameters”. These “self-channel response parameters” are thechannel response parameters of the OTFS waveform bursts that travelbetween the first device's wireless transmitter(s) and the firstdevice's own wireless receivers. Once this is obtained, the firstdevice, for example, can essentially perform “self-equalization” or“self-precoding) and use it's at least one processor and self-channelresponse parameters to digitally mitigate this coupling (cross-talk,interference).

Using Polarized OTFS Waveforms for Improved Channel Response ParameterDetermination

All electromagnetic waves, including the wireless (e.g. radio) wavesused for the present OTFS communication purposes, are polarized to someextent, but often the various directions of polarization are incoherentand thus the net polarization of the wireless waves may be minimal.

One interesting and useful aspect of polarization, however is that whenpolarized electromagnetic waves (wireless signals) reflect off ofvarious surfaces, the polarization of the reflected wireless signal maydiffer from the polarization of the incoming wireless signal dependingon the properties of the reflecting surface, and other factors such asthe geometry (e.g. various angles of incidence and reflection) of thesituation.

In the case of the OTFS technology disclosed herein, the fact thatpolarization may be altered by different reflecting materials anddifferent geometries of reflection can be further exploited to providestill more information regarding the structure of the multi-dimensionaldata channel, and to provide still more information regarding thechannel response parameters of the multidimensional data channel.

In this polarization enhanced embodiment, the OTFS transmitter(s) (e.g.102) transmit polarized originally transmitted OTFS waveform burstsaccording to at least one polarization direction. Here, however, assumethat at least some of the various wireless reflectors (e.g. 106) arealso polarization altering wireless reflectors that alter thepolarization of the various time delayed and Doppler frequency shiftedreflected wireless OTFS waveform bursts. Usually this polarizationalteration will be according to a first reflector polarization operator.Because this polarization alteration is also sensitive to relativeangles of the transmitter, receiver, and possibly other reflectors, insome embodiments this operator may be a polarization tensor, but forsimplicity and generality, we will refer to this a first reflectorpolarization operator.

In this polarization enhanced embodiment, the OTFS receiver(s) (e.g.104) may be further configured to detect the various directions ofpolarization in the received convoluted OTFS waveform bursts. Note thatthis polarization may not be uniform throughout the received burst, butmay vary in some frequency regions and time regions of the burstdepending on the structure of the data channel.

Thus, when the originally transmitted OTFS waveform bursts reflect offthe one wireless reflector(s), at least some of the originallytransmitted OTFS waveform bursts may also be polarization shiftedaccording to (for example) this first reflector polarization operator.

The OTFS receiver can then be configured to further detect thedirection(s) of polarization in the received channel convoluted OTFSwaveform bursts, and further use this polarization information tofurther determine the channel response parameters of themulti-dimensional data channel.

In effect, polarization changes can be used to enhance the contrastbetween the various reflectors. In most real-life situations, wherethere are usually multiple reflectors, it can be non-trivial (even usingOTFS techniques) to distinguish between them. Polarization methods makeit easier for the OTFS system to distinguish between the differentreflectors, and in turn construct a more accurate (e.g. more realistic)model of the channel response parameters. This in turn can allow thereceived signals to be deconvoluted better.

Using Location Determination Techniques to Retrieve Previously StoredChannel Response Parameters

In many situations, for example urban environments, the location ofnearly all of the major reflectors will tend to be relativelystationary, often over time periods of days, weeks, months, andsometimes even years. For example, consider a city. Although vehiclesmay move, otherwise the location of the major reflectors (e.g.buildings, bridges, other man-made structures) will not change at allfast. Indeed, often not much at all will happen until a building isconstructed or torn down.

Another factor is that often, at least with respect to cell towers orother infrastructure sources of wireless transmitters and receivers,even the cell towers (102) will tend to remain in place for long periodsof time, such as times of a year or even more.

This embodiment of the invention is thus based on the insight that,neglecting vehicles (which often are relatively small wirelessreflectors when compared to buildings), it is thus feasible to constructa “map” (e.g. location indexed computer database) of how the channelresponse parameters of a particular environment vary as a function ofthe location of the OTFS base station (which often will be in a fixedposition, here assume 102 m is a base station) and the location of theOTFS receiver or transceiver (104) or other OTFS mobile device (e.g.OTFS mobile transmitters, transceivers, and the like).

If this map of channel response parameters is stored in a computerdatabase (which can be located on the OTFS transmitter, the OTFSreceiver, or remotely), then a mobile OTFS device (104) can determineits present location by any means (including automatically making use ofGlobal Positioning Signals (GPS), internal navigation techniques,triangulation of radio sources, identities of known local WiFi hotspots,and the like) and then use its processor to look up previously storedchannel response parameters according to the mobile OTFS device'spresent location.

Similarly if the stationary cell tower (102 m) knows the location of themobile OTFS device (104), then the stationary cell tower (102 m) canalso look up the probable channel response parameters of the mobile OTFSdevice in the computer database (channel response parameter maps) aswell.

Thus using this scheme, even the first burst of communications between amobile OTFS device (104) and another OTFS device, such as a stationarycell tower (102) can start with reasonably optimized channel responseparameters on both ends. The systems can further optimize as time goeson (e.g. start with an initial model [set of channel responseparameters] that neglects moving reflectors, and then add movingreflectors later on in a later more refined set of improved channelresponse parameters).

Although to get the concept across, the initial discussion above used anexample of a stationary cell tower, in principle (although morecomplex), more complicated multi-dimensional channel response parametermaps (location indexed computer databases indexed by the location of twoor more OTFS devices) can also be constructed and used as needed.

Put alternatively, in some embodiments, the OTFS system may operate byfurther creating a map database of the channel response parameters ofthe multi-dimensional data channel at a plurality of transmitter andreceiver locations. The system can then determine the positions of atleast one wireless transmitter and at least one wireless receiver, anduse these positions to automatically search (usually using a processorfor this purpose) this map database and retrieve at least some channelresponse parameters of the multi-dimensional data channel at thesepositions. These channel response parameters can then be used for OTFScommunications purposes. For example, the map obtained channel responseparameters can be used to initialize or “bootstrap” the process, andthen supplemented by real time obtained channel response parametersduring the communications session.

Consider, for example, a mobile OTFS cell phone (e.g. 104) located faraway (e.g. at an extreme range) from its OTFS cell tower (102). If therange is too far, then even OTFS methods will eventually fail becausethe cell phone (104) and the tower (102) can't get lock on each other.However by using map obtained channel response parameters, the initial“let's get a lock” OTFS handshaking channel response parameters can beused to optimize the signal enough to at least get communicationsstarted. Further optimization can then follow.

Methods of Operating OTFS Transmitters

It should be evident that the various methods and systems describedherein, which apply to wireless OTFS transmitters, wireless OTFSreceivers, and methods in which wireless OTFS receivers and wirelessOTFS transmitters can cooperate to improve signal transmission betweenthe transmitters, thus of course also apply to methods of operating oneor more OTFS wireless transmitters, as well as methods of operating oneor more OTFS wireless receivers.

In general, at the transmitter level, the invention thus covers variousmethods of configuring, constructing, and operating one or more OTFSwireless transmitter devices, as well as the OTFS wireless transmitterdevices themselves.

As a common denominator, the basic transmitter method, which can then beextended and elaborated upon according to the previously describedembodiments, is a method of operating at least one OTFS wirelesstransmitter device. The wireless transmitter can be a softwareconfigured wireless transmitter (e.g. constructed from FPGA/DSP,suitable transmitter processors, and transmitter according to themethods of Harris or other methods). As before, these various OTFSwireless transmitter devices will have their respective locations andvelocities, and each will typically be configured to automaticallywirelessly transmit various symbols through space (e.g. themulti-dimensional data channel, with its associated wireless reflectors,and channel response parameters) to one or more wireless OTFS receiverdevices. These wireless OTFS receivers will also each have their ownrespective locations and velocities.

More specifically, as previously discussed, the OTFS transmitter deviceswill generally comprise at least one processor (often one or moremicroprocessors or digital signal processors), memory, and least oneprocessor-controlled wireless transmitter component configured totransmit a plurality of wireless signals simultaneously at a pluralityof frequencies. As previously discussed, the processor(s) andtransmitter(s) are often configured to spread each OTFS symbol in theplurality of OTFS symbols throughout a plurality of mutually orthogonaltime shifted and frequency shifted wireless OTFS waveform bursts, andthen use the antenna(s) to transmit these bursts. In some embodiments,the transmitter may further transmit various error detection/correctionsymbols, pilot signals, polarization schemes, and use various MIMOmethods and other methods described previously. The transmitter may alsofurther vary the range of OTFS time shifts and frequency shifts,duration of the burst length, burst bandwidth, and other characteristicsas described previously. Often the transmitter may have one or moreassociated wireless receivers, which may be OTFS wireless receivers orother type wireless receiver, configured to receive signals originatingfrom other OTFS transmitters operating in conjunction with distant OTFSreceiver devices, and use information obtained from these other OTFStransmitters to adjust the various aspects of transmitter operationdescribed previously.

Thus the basic transmitter scheme can then be supplemented by variouscombinations and permutations of the various methods describedpreviously in this disclosure.

Methods of Operating OTFS Receivers

Similarly, it should also be evident that the various methods andsystems described herein, which apply to wireless OTFS transmitters,wireless OTFS receivers, and methods in which wireless OTFS receiversand wireless OTFS transmitters can cooperate to improve signaltransmission between the transmitters, thus of course also apply tomethods of operating one or more OTFS wireless receivers, as well as thereceiver devices themselves.

In general, at the receiver level, the invention thus covers variousmethods of designing, configuring, constructing, and operating one ormore OTFS wireless receiver devices.

As a common denominator, the basic receiver method, which can also thenbe extended and elaborated upon according to the previously describedembodiments, can be a method of operating at least one OTFS wirelessreceiver device. As before, these receiver devices will generally eachhave their own respective device locations and velocities, and will alsogenerally be configured to automatically wirelessly receive a pluralityof symbols transmitted through a multi-dimensional data channel from oneor more of the previously described OTFS wireless transmitter devices(which of course have their own various locations and velocities). TheOTFS receivers will then decode these symbols after the waveforms havebeen distorted by the previously described reflectors (which can havelocations, velocities, and one or more coefficients, parameters, oroperators of wireless reflection) and channel response parameters.

Thus, as previously described, the OTFS wireless waveform bursts travelover at least one path to the receiver (e.g. at least one of a:originally transmitted wireless OTFS waveform bursts traveling directlyfrom the wireless transmitter(s) to the OTFS wireless receiver device(s)as direct wireless OTFS waveform bursts; and/or b: originallytransmitted OTFS waveform bursts reflecting off the wirelessreflector(s) before reaching the OTFS wireless receiver device(s)thereby producing time delayed and Doppler frequency shifted reflectedwireless OTFS waveform bursts at the OTFS wireless receiver device(s),thus producing, at the receiver, a combination of these direct burstsand any said reflected bursts thus producing the channel convoluted OTFSwaveform bursts described previously).

Here as before, the channel response parameters of the multi-dimensionaldata channel are determined by at least the relative positions, relativevelocities, and properties of the wireless transmitter device(s), OTFSwireless receiver device(s), and wireless reflector(s).

To handle this, the OTFS wireless receiver will typically comprise atleast one processor-controlled wireless receiver component configured toreceive wireless signals at a plurality of frequencies, at least oneprocessor, memory, and at least one antenna. The wireless receivercomponent can be a software configured receiver (e.g. constructed fromFPGA/DSP, suitable receiver processors, and receiver software accordingto the methods of Harris or other methods), or other type receiver.

The receiver device's processor will often be configured (often withsuitable software), to use the wireless receiver components, antenna(s)and memory to receive the convoluted OTFS waveform bursts, and determinethe channel response parameters. In some embodiments, this may beassisted by the error detection/correction methods, pilot signalmethods, MIMO methods and other methods described previously.

Typically at least one receiver device processor will be furtherconfigured (often using software) to use these channel responseparameters to compute suitable deconvolution parameters, and use thesedeconvolution parameters to then deconvolute the channel convoluted OTFSwaveform bursts. This results in at least an approximation (ideally avery good approximation) of the originally transmitted OTFS waveformbursts. Then at least one receiver device processor will usually thenmathematically extract (or otherwise solve for) the various originallytransmitted OTFS symbols from this approximation of the originalsignals, and thus the various originally transmitted OTFS symbols thatcontain the data payload will then be received.

If the remote OTFS transmitter transmitting to the receiver hastransmitted various error detection/correction symbols, pilot signals,or used various MIMO methods and other methods described previously tocommunicate with the OTFS receiver, then often the OTFS receiver will befurther configured to use these methods to improve performance asdescribed previously. If the remote OTFS transmitter has varied therange of OTFS time shifts and frequency shifts, duration of the burstlength, burst bandwidth, polarization schemes and other characteristicsas described previously, then often the OTFS receiver will be configuredto work with or compensate for these changes.

Often the OTFS receiver will be a transceiver with one or more of itsown associated wireless transmitters, which may be OTFS wirelesstransmitters or other type wireless transmitters, configured to transmitsignals to other OTFS receivers operating in conjunction with distantOTFS transmitter devices (i.e. the distant OTFS transmitters will oftenalso be transceivers). The OTFS receiver may use its own transmitters totransmit information and suggestions to the distant OTFS transmitterdevices to adjust various aspects of the remote OTFS transmitteroperation as described previously.

Regarding Optimizing OTFS Settings to Fit the Situation at Hand

The most common applications of the invention will be on Earth, usuallyat regions near the ground, where there will be a breathable amount ofair, and other natural atmospheric phenomenon such as clouds, rain, andhail. For many wireless frequencies, radio waves pass through thisnatural atmospheric phenomenon with little interference, and thus oftenthe effects of the intervening air and natural atmospheric phenomenoncan be ignored. For higher frequency radio signals, this naturalphenomenon can be treated by the system as sources of additionalwireless signal attenuation or additional wireless reflectors as thecase may be.

As previously discussed, the most common applications of the inventionwill also often be in either urban or rural environments on Earth ornear earth, where relevant reflectors (e.g. various buildings, naturalor artificial structures, vehicles and the like) can be assumed to havecertain geometries, and spacing, as well as to operate within certainassumes ranges of speeds (e.g. generally 0-100 miles per hour forvehicles, between 0-1000 miles per hour for airplanes, and the like). Tosome extent, these assumptions may be used to fine-tune variousparameters (e.g. various burst lengths, time shifts, frequency shiftsand the like) that will be discussed shortly. Conversely, a version ofthe invention designed to operate in a very different environment, suchas for commercial or military aviation at higher altitudes, or in orbitor outer space, may have various parameters that are fine-tuned to copewith a much broader range of potential velocities distances, andreflector spacing.

Combining Previously Discussed Methods to Produce a High PerformanceSystem

FIG. 7 shows how the various embodiments of the invention—OTFStransmitters (e.g. 102, 102 m, 700), OTFS receivers (e.g. 104, 104 m,740), and the previously discussed schemes, such as OTFS time shifts,frequency shifts, polarization, burst characteristics, use of errorcodes, pilot symbols, polarization schemes, MIMO antennas, maps ofchannel response parameters and the like can all work together, eitherall combined, or with various permutations of various specific methods,to produce a unified OTFS wireless communications system designed toprovide robust and fade resistant communications even when operating ina difficult and constantly changing environment.

FIG. 7 can best be understood as a software flow chart showing oneembodiment by which OTFS transmitter processors and OTFS receiverprocessors can vary essentially any and all of the previously discussedmodes of operation, in almost any combination, in order to dynamicallyoptimize OTFS wireless transmissions, even within a singlecommunications session.

For example, consider how an OTFS transmitter, such as (102 or 102 m),can be controlled at the software level (700) using, for example, one ormore OTFS transmitter processors and suitable control software. At thebeginning of a wireless OTFS communications session, the OTFStransmitter may use its processor to obtain initial OTFS parameters,such as an initial set of OTFS channel response parameters (702) fromvarious sources including the transmitter's memory and/or the previouslydescribed local or remote map database (704) (e.g. the transmitter canwirelessly transmit its GPS location to a remote map server, and receiveback various location specific OTFS parameters such as an initial set ofchannel response parameters). The OTFS transmitter can then use thisinitial set of OTFS parameters to start OTFS wireless transmissions toOTFS receiver (104, 104 m, 740). OTFS receiver (104, 104 m, 740) canalso initialize its initial set of OTFS parameters (742) using similarreceiver memory and/or map server methods (744). Here of course, forsuch GPS assisted mapping schemes to be used, the device, be it OTFStransmitter and or OTFS receiver, will have GPS units or other locationdetermination circuits.

In this example, for simplicity, assume that the transmitter(transmitter processor) is configured (e.g. often by software) to beable to change various OTFS transmission variables on a per data framemethod, but usually not within a data frame. (Other schemes with finergranularity, e.g. changes in various OTFS transmission variables at afiner level within an OTFS data frame, can also be used.)

After initialization, the OTFS transmitter software (700) can enter in atransmission loop (706), (708), (710). This loop will typically progressin various iterations as multiple data frames are transmitted until alldata frames in a communications session have been transmitted. Inparticular, the transmitter can start the first iteration of loop (708)by configuring the various OTFS modulation schemes and burstcharacteristics as best it can with available data (e.g. the latest OTFSparameters).

Next (710), in this example on a per data frame basis, the OTFStransmitter processor and software (700) can set up various error codeschemes appropriate for the situation at hand, as well as use availableinformation to adjust the settings of any transmitter MIMO antennas (110a-110 d). Typically as the communication session continues over multipledata frames, these various settings become further optimized for theparticular data channel conditions.

The wireless OTFS transmitter is now ready to start this iteration'stask of packaging the actual useful data (e.g. payload) (712) fortransmission. To do this, the transmitter processor and software (700)can embed the payload data along with various pilot symbols and errorcorrection symbols into suitable OTFS data frames (714), and thenmodulate and transmit (716). The originally transmitted wireless OTFSwaveform bursts (718) travel to the wireless OTFS receiver (104, 104 m)along various direct OTFS waveform burst paths (e.g. 112) and variousreflected OTFS waveform burst paths (e.g. 114 a, 114 b), and areeventually received by the receiver and handled by receiver software(740).

In many embodiments, OTFS wireless transmitter (102, 102 m) will haveits own receiver, which may be an OTFS wireless receiver, but which canalso be other types of receivers. Assuming that this transmitter is alsoequipped with its own local wireless receiver, and that OTFS receiver(104, 104 m) is also equipped with its own local transmitter, then insome optional embodiments, OTFS transmitter (700) can also receivechannel response parameter feedback and error code feedback (720) fromOTFS receiver software (740) and receiver (102, 102 m) and handle thisaccording to transmitter's software (722). The OTFS transmitter software(700) and associated hardware can then use whatever information it hasaccumulated to update the various previously discussed OTFS transmitterparameters (710), and in the next iteration, the transmission loop (706,708, 710) can then transmit the next data frame with either the same setof transmission variables or different transmission variables asconditions warrant. This process again will generally be done by atleast one transmitter processor and suitable software.

The OTFS receiver side of the process generally performs the counterpartof the previously discussed OTFS transmitter functions. The receiver(104, 104 m) will also generally be under the control of at least onereceiver processor and receiver software (740). Receiver software (740)and associated receiver hardware may also initialize the receiver'sreception of wireless OTFS data frames by first retrieving (742)suitable initial OTFS parameters from either the receiver's memory (744)and/or by using the previously described receiver memory and/or mapserver methods (744).

The OTFS receiver software (740) and associated hardware can then enterinto its own receiver loop (746, 748, 750) iterations. In this example,for simplicity, assume that the OTFS receiver (receiver processor) isconfigured (e.g. often by suitable receiver software 740) to be able tochange its various OTFS reception variables on a per-data-frame basis aswell (or other schemes as desired). (As with the transmitter, otherreceiver schemes with finer granularity, e.g. changes in various OTFStransmission variables at a finer level within an OTFS data frame, canalso be used.)

The OTFS receiver will receive (often on a per data frame basis) the nowchannel convoluted OTFS waveform bursts (718) which are the combinationof any direct wireless OTFS waveform bursts (112, 112 a) and anyreflected wireless OTFS waveform bursts (114 b). The receiver will thenuse its one or more processors and software (740) to decode any pilotsignals that the transmitter may have embedded in the transmittedsignals (752), and otherwise determine the channel response parametersof the multi-dimensional data channel at that time. The receiver canthen use these channel response parameters and, with suitable error codeand correction, decode the data payload (754) and this received data(756) can be stored in memory or output for subsequent use.

If the receiver (104, 104 m) has its own local transmitter, the receiversoftware (740) and processor can direct the receiver's local transmitterto transmit information pertaining to the receiver determined channelresponse parameters other information, such as error code feedback,receiver MIMO settings and capability (if any) to the transmitter (102,102 m) where it can be received by the transmitter's local receiver andinterpreted by the transmitter's software (720). Thus if the transmitterhas its own local receiver, the transmitter can use its local receiverto receive this data and use it to refine its own settings forsubsequent transmitted data frames.

The receiver software (740) and processor can also use informationderived from the channel response parameters and error codes todetermine how to best refine the adjustment of its various MIMO antennas(if any) for receiving the next data frame (758).

Many other OFTS receiver and transmitter operating schemes are alsopossible. The main purpose of FIG. 7 is to give one specific example ofhow the various methods disclosed herein may be combined (in variouscombinations, and not all methods need be used) to produce a robust andhigh performance wireless communication system.

Further discussion of GPS techniques:

Note further that GPS or other location determination techniques mayalso be used for other purposes, such as helping to better determinetime synchronization between the transmitter and receiver. Here forexample, by knowing the relative locations of the transmitter andreceiver, the distance between the transmitter and receiver can thus bedetermined. By making use of fundamental constants, such as the speed oflight, the effect of transmission delay on timing can thus beautomatically determined, and this transmission timing delay can thus beused for more accurate timing synchronization throughout the system.

Further Details of OTFS Waveform Structure and OTFS Burst Structure

A variety of methods may be used to generate OTFS waveforms. Here themain criteria is that each data symbol is distributed, in a lossless andinvertible manner, across a plurality of distinguishable (e.g. usuallymutually orthogonal) waveforms over a plurality of different times anddifferent frequencies chosen according to the time delay andDoppler-shift channel response parameters of the wirelessmulti-dimensional data channel.

In some embodiments, the OTFS waveforms may be produced and structuredaccording to methods previously discussed in patent applications U.S.61/349,619, U.S. Ser. No. 13/177,119, U.S. Ser. No. 13/430,690 and aswell as U.S. Pat. No. 8,547,988; the complete contents of which areincorporated herein by reference in their entirety. Some specificexamples of some of these embodiments are discussed below.

In some embodiments, at the transmitter end, a microprocessor controlledtransmitter may package a series of different symbols “d” (e.g. d₁, d₂,d₃ . . . ) for transmission by repackaging or distributing the symbolsinto various elements of various N·N matrices [D] by, for exampleassigning d₁ to the first row and first column of the [D] matrix (e.g.d₁=d_(0,0)), d₂ to the first row second column of the [D] matrix (e.g.d₂=d_(0,1)) and so on until all N·N symbols of the [D] matrix are full.Here, once we run out of d symbols to transmit, the remaining [D] matrixelements can be set to be 0 or other value indicative of a null entry.

The various primary waveforms used as the primary basis for transmittingdata, which here will be called “tones” to show that these waveformshave a characteristic sinusoid shape, can be described by an N·N InverseDiscrete Fourier Transform (IDFT) matrix [W], where for each element win [W],

$w_{j,k} = e^{\frac{i\; 2\pi\;{jk}}{N}}$or alternatively w_(j,k)=e^(ijθ) ^(k)

w_(j, k) = e^(i j θ_(k))  or   w_(j, k) = [e^(i θ_(k))]^(j).Thus the individual data elements d in [D] are transformed anddistributed as a combination of various fundamental tones w by a matrixmultiplication operation [W]*[D], producing a tone transformed anddistributed form of the data matrix, here described by the N·N matrix[A], where [A]=[W]*[D].

To produce the invention's N time shifted and N frequency shiftedwaveforms, the tone transformed and distributed data matrix [A] is thenitself further permuted by modular arithmetic or “clock” arithmetic,creating an N·N matrix [B], where for each element of b of [B],b_(i,j)=a_(i,(i+j)mod N). This can alternatively be expressed as[B]=Permute([A])=P(IDFT*[D]). Thus the clock arithmetic controls thepattern of time and frequency shifts.

A unitary matrix [U] can then be used to operate on [B], producing anN·N transmit matrix [T], where [T]=[U]*[B], thus producing a N² sizedset of all permutations of N time shifted and N frequency shiftedwaveforms determined according to an encoding matrix [U]. Putalternatively, the N·N transmit matrix [T]=[U]*P(IDFT*[D]).

Then, typically on a per column basis, each individual column of N isused to further modulate a frequency carrier wave (e.g. if we aretransmitting in a range of frequencies around 1 GHz, the carrier wavewill be set at 1 GHz), and each column the N·N matrix [T] which has Nelements, thus produces N symbol-weighted time shifted and frequencyshifted waveforms for each data symbol. Effectively then, thetransmitter is transmitting the sum of the N symbol-weighted timeshifted and frequency shifted waveforms from one column of [T] at a timeas, for example, a composite waveform over a time block of data.Alternatively the transmitter could instead use a different frequencycarrier wave for the different columns of [T], and thus for exampletransmit one column of [T] over one frequency carrier wave, andsimultaneously transmit a different column of [T] over a differentfrequency carrier wave, thus transmitting more data at the same time,although of course using more bandwidth to do so. This alternativemethod of using different frequency carrier waves to transmit more thanone column of [T] at the same time will be referred to as frequencyblocks, where each frequency carrier wave is considered its ownfrequency block.

Thus, since the N·N matrix [T] has N columns, the transmitter willtransmit the N² summation-symbol-weighted time shifted and frequencyshifted waveforms, structured as N composite waveforms, over anycombination of N time blocks or frequency blocks.

On the receiver side, the transmit process is essentially reversed.Here, for example, a microprocessor controlled receiver would of coursereceive the various columns [T] (e.g. receive the N composite waveforms,also known as the N symbol-weighted time shifted and frequency shiftedwaveforms) over various time blocks or frequency blocks as desired forthat particular application. If for example there is a lot of availablebandwidth and time is of the essence, then the transmitter willtransmit, and the receiver will receive, the data as multiple frequencyblocks over multiple frequency carrier waves. On the other hand, ifavailable bandwidth is more limited, and/or time (latency) is lesscritical, then the transmit will transmit and the receiver will receiveover multiple time blocks instead.

So effectively the receiver tunes into the one or more frequency carrierwaves, and over the number of time and frequency blocks set for thatparticular application eventually receives the data or coefficients fromoriginal N·N transmitted matrix [T] as an N·N receive matrix [R] where[R] is similar to [T], but may not be identical due to variouscommunications impairments.

The microprocessor controlled receiver then reverses the transmitprocess as a series of steps that mimic, in reverse, the originaltransmission process. The N·N receive matrix [R] is first decoded byinverse decoding matrix [U^(H)], producing an approximate version of theoriginal permutation matrix [B], here called [B^(R)], where[B^(R)]=([U^(H)]*[R]).

The receiver then does an inverse clock operation to back out the datafrom the time shifted and frequency shifted waveforms (or tones) bydoing an inverse modular mathematics or inverse clock arithmeticoperation on the elements of the N·N [B^(R)] matrix, producing, for eachelement b^(R) of the N·N [B^(R)] matrix, a_(i,j) ^(R)=b_(i,(j-i)mod N)^(R). This produces a “de-time shifted and de-frequency shifted” versionof the tone transformed and distributed form of the data matrix [A],here called [A^(R)]. Put alternatively, [A^(R)]=Inverse Permute([B^(R)]), or [A^(R)]=P⁻¹([U^(H)]*[R]).

The receiver then further extracts at least an approximation of theoriginal data symbols d from the [A^(R)] matrix by analyzing the [A]matrix using an N·N Discrete Fourier Transform matrix DFT of theoriginal Inverse Fourier Transform matrix (IDFT).

Here, for each received symbol d^(R), the d^(R) are elements of the N·Nreceived data matrix [D^(R)] where [D^(R)]=DFT*A^(R), or alternatively[D^(R)]=DFT*P⁻¹([U^(H)]*[R]).

Thus the original N² summation-symbol-weighted time shifted andfrequency shifted waveforms are subsequently received by a receiverwhich is controlled by the corresponding decoding matrix U^(H) (alsorepresented as [U^(H)]) The receiver (e.g. the receiver's microprocessorand associated software) uses this decoding matrix [U^(H)] toreconstruct the various transmitted symbols “d” in the one or moreoriginally transmitted N·N symbol matrices [D] (or at least anapproximation of these transmitted symbols).

Alternatively, in some in some embodiments, these “tones” may benarrow-band subcarriers, such as OFDM subcarriers. Alternative encodingand decoding schemes may be used so that, for example, an N×M datamatrix can be transmitted over M narrow-band subcarriers over N timeperiods.

There are several ways to correct for distortions caused by the signalimpairment effects of echo reflections and frequency shifts. One way is,at the receiver front end, utilize the fact that the time shifted andfrequency shifted waveforms or “tones” form a predictable time-frequencypattern, and a “dumb” deconvolution device situated at the receiver'sfront end can recognize these patterns, as well as the echo reflectedand frequency shifted versions of these patterns, and perform theappropriate deconvolution by a pattern recognition process.Alternatively the distortions may be mathematically corrected by thereceiver's software, here by doing suitable mathematical transformationsto essentially determine the echo reflected and frequency shiftingeffects, and solve for these effects. As a third alternative, once, byeither process, the receiver determines the time and frequencydeconvolution parameters of the communication media's particular timeand frequency distortions, the receiver may transmit a command to thetransmitter to instruct the transmitter to essentially pre-compensate orpre-encode for these effects. That is, if for example the receiverdetects an echo, the transmitter can be instructed to transmit in amanner that offsets this echo, and so on.

Echo reflections and frequency shifts can blur or impair or distort atransmitted signal by inducing additive noise. These distortions can bemodeled as a 2-dimensional filter acting on the data array. This filterrepresents, for example, the presence of multiple echoes with timedelays and Doppler shifts. To reduce these distortions, the signal caneither be pre-equalized before receiver subsequent receiver processing,or alternatively post-equalized after the D^(R) matrix has beenrecovered. This equalization process may be done either by analog ordigital methods. The equalized form of the received D matrix, whichideally will completely reproduce the original D matrix, is termedD_(eq).

In some embodiments, an adaptive linear equalizer may be used to correctfor such distortions. This adaptive linear equalizer can function ateither step, optionally as a more analog method or step, but moregenerally as a more digital and mathematical process.

The equalizer may, in some embodiments operate according to a functionsuch as:

${Y(k)} = {{\sum\limits_{L = {Lc}}^{Rc}{{C(l)}*{X\left( {k - l} \right)}}} + {{\eta(k)}.}}$

In other embodiments, channel response parameters obtained by use ofOTFS pilot symbols (see FIGS. 2 and 3 and related discussion mayalternatively or additionally be used to assist in this equalization(deconvolution) process.

The invention claimed is:
 1. An automated method of wirelesslytransmitting a plurality of symbols through a multi-dimensional datachannel connecting at least one wireless transmitter and at least onewireless receiver; said multi-dimensional data channel comprising atleast two dimensions of space and one dimension of time; saidmulti-dimensional data channel further comprising at least one wirelessreflector, each said at least one wireless reflector comprising areflector location, velocity, and at least one coefficient of wirelessreflection; each said at least one wireless transmitter comprising awireless transmitter location and velocity; each said at least onewireless receiver comprising a wireless receiver location and velocity;said method comprising: at least for said symbols that comprise datasymbols, and where there are a plurality of such data symbols, using atleast one processor to transmit said data symbols as originallytransmitted wireless waveform bursts; wherein upon propagation throughsaid multi-dimensional data channel, said originally transmittedwireless waveform bursts travel over at least one path, said at leastone path, comprising at least one of: a: originally transmitted wirelesswaveform bursts traveling directly from said at least one wirelesstransmitter to said at least one wireless receiver as direct wirelesswaveform bursts; and/or b: originally transmitted waveform burstsreflecting off of said at least one wireless reflector before reachingsaid at least one wireless receiver, thereby producing time delayed andDoppler frequency shifted reflected wireless waveform bursts at said atleast one wireless receiver; wherein at said at least one wirelessreceiver, a resulting combination of any said direct wireless waveformbursts and any said reflected wireless waveform bursts produces channelconvoluted waveform bursts; at said at least one wireless receiver,receiving said channel convoluted waveform bursts; using at least oneprocessor to determine channel response parameters of saidmulti-dimensional data channel between said at least one wirelesstransmitter and said at least one wireless receiver, wherein saidchannel response parameters of said multi-dimensional data channel arecreated by at least relative positions, relative velocities, andproperties of said at least one wireless transmitter, said at least onewireless receiver, and said at least one wireless reflector; using saidchannel response parameters and at least one processor to deconvolutereceived channel convoluted waveform bursts, thereby deriving at leastan approximation of said originally transmitted waveform bursts; usingat least one processor to extract said plurality of data symbols fromsaid approximation of said originally transmitted waveform bursts;thereby transmitting at least some of said data symbols between said atleast one wireless transmitter and at least one wireless receiver. 2.The method of claim 1, further using said at least one transmitter andat least one processor to transmit at least one pilot symbol as at leastone wireless pilot symbol waveform burst at at-least one defined timeand frequency; wherein the direct and reflected versions of said atleast one wireless pilot symbol waveform burst reach said at least onewireless receiver as at least one channel convoluted pilot symbolwaveform burst; at said at least one wireless receiver, receiving saidat least one channel convoluted pilot symbol waveform burst, and usingat least one processor to determine the channel response parameters ofsaid multi-dimensional data channel connecting said at least onewireless transmitter and at least one wireless receiver; andsubsequently using said channel response parameters to furtherdeconvolute the received channel convoluted waveform bursts.
 3. Themethod of claim 1, wherein at least some of said symbols comprise errordetection or error correction symbols; further using at least oneprocessor at said at least one receiver to use said error detection orerror correction symbols to detect when symbol transmission errorsexceed a predetermined acceptable error level, and to automaticallyinform said receiver or said transmitter that said channel responseparameters are suboptimum, and to initiate corrective action; and/orfurther using at least one processor and said at least one receiver touse said error detection or error correction symbols to automaticallycorrect errors in other data symbols.
 4. The method of claim 1, whereinat least one of said wireless transmitter and said wireless receiverhave multiple antennas, said multiple antennas positioned at differentlocations on or near said at least one wireless transmitter and saidwireless receiver, and said multiple antennas sharing the same velocityof their respective wireless transmitter or wireless receiver; furtherusing said multiple antennas to perform at least one of furtherdetermining said channel response parameters and shaping at least aspatial distribution of said transmitted or received wireless waveformbursts.
 5. The method of claim 1, wherein at least one of said wirelesstransmitter and said wireless receiver have multiple antennas, saidmultiple antennas positioned at different locations on or near said atleast one wireless transmitter and said wireless receiver, and saidmultiple antennas sharing the same velocity of their respective wirelesstransmitter or wireless receiver; wherein said multiple antennas aredivided into at least a first subset of antennas and a second subset ofantennas; and said first subset of said multiple antennas transmits orreceives a first set of wireless waveform bursts that differs from asecond set of wireless waveform bursts transmitted or received by saidsecond subset of antennas.
 6. The method of claim 1, wherein at leastone of said wireless transmitter and said wireless receiver areconfigured in a first full duplex device, and wherein at least one ofsaid wireless transmitter and said wireless receiver are configured in asecond full duplex device; on at least said first full duplex device,further controlling coupling between said first full duplex device's atleast one wireless transmitter and said first full duplex device's atleast one wireless receiver so as to mitigate interference between saidfirst full duplex device's at least one wireless transmitter and saidfirst full duplex device's at least one wireless receiver whiletransmitting to said second full duplex device, and simultaneously alsooptimizing a sensitivity of said first full duplex device's at least onewireless receiver while receiving from said second full duplex device'sat least one wireless transmitter; wherein said controlling coupling isdone by also obtaining self-channel response parameters of waveformbursts or pilot symbol waveform bursts traveling between said first fullduplex device's at least one wireless transmitter and said first fullduplex device's at least one wireless receiver; and using said firstfull device's at least one processor and said self-channel responseparameters to digitally mitigate said interference.
 7. The method ofclaim 1, wherein said at least one transmitter transmits polarizedoriginally transmitted waveform bursts or pilot symbol waveform burstsaccording to at least one direction of polarization; said at least onewireless reflector is a polarization altering wireless reflector thatalters the polarization of said time delayed and Doppler frequencyshifted reflected wireless waveform bursts or pilot symbol waveformbursts according to a first reflector polarization operator; said atleast one receiver is further configured to detect at least onedirection of polarization in said received convoluted waveform bursts orpilot symbol waveform bursts; wherein when said originally transmittedwaveform bursts or pilot symbol waveform bursts reflect off of said atleast one wireless reflector, at least some of said originallytransmitted waveform bursts or pilot symbol waveform bursts are alsopolarization shifted according to said first reflector polarizationoperator; further using said at least one direction of polarization insaid received channel convoluted waveform bursts or pilot symbolwaveform bursts to further determine the channel response parameters ofsaid multi-dimensional data channel.
 8. The method of claim 1 furthercreating a map database of the channel response parameters of saidmulti-dimensional data channel at a plurality of transmitter andreceiver locations; determining positions of said at least one wirelesstransmitter and said at least one wireless receiver; and using positionsof said at least one wireless transmitter and said at least one wirelessreceiver to search said map database and retrieve at least some channelresponse parameters of said multi-dimensional data channel at saidpositions of said at least one wireless transmitter and/or said at leastone wireless receiver.
 9. A method of operating at least one wirelesstransmitter device, each said at least one wireless transmitter devicehaving a wireless transmitter device location and velocity, each said atleast one wireless transmitter device configured to automaticallywirelessly transmit a plurality of symbols through a multi-dimensionaldata channel to at least one wireless receiver device with a wirelessreceiver device location and velocity; said multi-dimensional datachannel comprising at least two dimensions of space and one dimension oftime; wherein said at least some of said plurality of symbols comprise aplurality of data symbols; said multi-dimensional data channel furthercomprising at least one wireless reflector, each said at least onewireless reflector comprising a reflector location, velocity, and atleast one coefficient of wireless reflection; wherein channel responseparameters of said multi-dimensional data channel are determined by atleast relative positions, relative velocities, and said coefficients ofwireless reflection of each said at least one wireless transmitterdevice, said at least one wireless receiver device, and said at leastone wireless reflector; each said at least one transmitter devicecomprising: at least one processor, memory, at least oneprocessor-controlled wireless transmitter component configured totransmit wireless signals at a plurality of frequencies, and at leastone antenna; and using said at least one antenna to wirelessly transmitsaid symbols as wireless waveform bursts, thereby producing originallytransmitted wireless waveform bursts.
 10. The method of claim 9, whereinsaid channel response parameters are at least initially determined byretrieving said channel response parameters from memory; and whereinsaid channel response parameters are subsequently at least partiallydetermined based upon feedback obtained from a wireless receiver thathas received said transmitted symbols.
 11. A method of operating atleast one wireless receiver device, each said at least one wirelessreceiver device having a wireless receiver device location and velocity,each said at least one wireless receiver device configured toautomatically wirelessly receive a plurality of symbols transmittedthrough a multi-dimensional data channel by least one wirelesstransmitter device with a wireless transmitter device location andvelocity; wherein at least some of said plurality of symbols comprise aplurality of data symbols, previously transmitted as a pluralityoriginally transmitted wireless waveform bursts; said multi-dimensionaldata channel comprising at least two dimensions of space and onedimension of time; said multi-dimensional data channel furthercomprising at least one wireless reflector, each said at least onewireless reflector comprising a reflector location, velocity, and atleast one coefficient of wireless reflection; wherein upon propagationthrough said multi-dimensional data channel, said originally transmittedwireless waveform bursts travel over at least one path, said at leastone path, comprising at least one of: a: originally transmitted wirelesswaveform bursts traveling directly from said at least one wirelesstransmitter to said at least one wireless receiver device as directwireless waveform bursts; and/or b: originally transmitted waveformbursts reflecting off of said at least one wireless reflector beforereaching said at least one wireless receiver device, thereby producingtime delayed and Doppler frequency shifted reflected wireless waveformbursts at said at least one wireless receiver device; wherein at said atleast one wireless receiver device, a resulting combination of any saiddirect wireless waveforms bursts and any said reflected wirelesswaveform bursts produces channel convoluted waveform bursts; whereinchannel response parameters of said multi-dimensional data channel aredetermined by at least relative positions, relative velocities, andproperties of said at least one wireless transmitter device, saidwireless receiver device, and said at least one wireless reflector; saidwireless receiver device comprising: at least one processor-controlledwireless receiver component configured to receive wireless signals at aplurality of frequencies, at least one processor, memory, and at leastone antenna; said at least one processor configured to use said at leastone wireless receiver component, at least one antenna, and memory toreceive said convoluted waveform bursts or pilot symbol waveform bursts,and determine channel response parameters; said at least one processorfurther configured to use said channel response parameters and saidmemory to deconvolute received channel convoluted waveform bursts,thereby deriving at least an approximation of said originallytransmitted waveform bursts; said at least one processor furtherconfigured to use said memory to extract said plurality of data symbolsfrom said approximation of said originally transmitted waveform bursts,thereby receiving said plurality of data symbols.
 12. The method ofclaim 11, wherein said channel response parameters are at leastinitially determined by retrieving said channel response parameters frommemory; and further transmitting feedback pertaining to said channelresponse parameters to a transmitter that has transmitted said pluralityof symbols.